In order to evaluate the applicability of the pore-fracture structure fractal characterizations in coal reservoirs and confirm the internal relationships between the porosity, permeability, coal metamorphic grade, and pore-fracture structure, the pore-fracture features of 21 middle-high rank coal samples from Anhe, Jiaozuo, and Huaibei coalfields in northern China were investigated using a low-field nuclear magnetic resonance (NMR). All the coal samples are characterized by low moisture content (M ad), low and medium ash yield (A ad), and high vitrinite (V) in coal maceral. The adsorption space fractal dimension (D A) is positively correlated with the Langmuir volume (V L) under the three-peak transverse relaxation time (T 2) spectrum. The fractal dimension of all effective T 2 points under saturated water (D NMR) is positively correlated with V L and the adsorption pore volume, but negatively correlated with the volume ratio of seepage pores and fractures. The free flow space fractal dimension (D M) is negatively correlated with the porosity of full saturated water (ΦF) and the porosity of movable water (ΦM). There is a negative correlation between ΦF and the seepage space fractal dimension (D S) in the coal samples with one-peak and two-peak T2 spectra, but a positive correlation can be found with the three-peak T2 spectrum. Therefore, it is necessary to consider the types of T2 spectral peak as a prerequisite to analyze the correlations between pore-fracture parameters and NMR fractal dimensions. With the increase of coal rank, the adsorption pore content, ΦF, and bulk volume immovable (BVI) fraction first increase and then decrease, whereas the seepage pore content, fracture development, bulk volume movable (BVM) fraction, and BVM/BVI first decrease and then increase. The inflection points of these changes correspond to the maximum vitrinite reflectance (R o,max) at 2.6-2.8%, which would be attributed to the third coalification jump. Generally, D A is the fractal dimension representing the coal pore surface, and D S and D M are closely related to the pore structure. Furthermore, D NMR not only represents the roughness of the pore surface but also the complexity of the pore structure.
In order to evaluate the applicability of the pore-fracture structure fractal characterizations in coal reservoirs and confirm the internal relationships between the porosity, permeability, coal metamorphic grade, and pore-fracture structure, the pore-fracture features of 21 middle-high rank coal samples from Anhe, Jiaozuo, and Huaibei coalfields in northern China were investigated using a low-field nuclear magnetic resonance (NMR). All the coal samples are characterized by low moisture content (M ad), low and medium ash yield (A ad), and high vitrinite (V) in coal maceral. The adsorption space fractal dimension (D A) is positively correlated with the Langmuir volume (V L) under the three-peak transverse relaxation time (T 2) spectrum. The fractal dimension of all effective T 2 points under saturated water (D NMR) is positively correlated with V L and the adsorption pore volume, but negatively correlated with the volume ratio of seepage pores and fractures. The free flow space fractal dimension (D M) is negatively correlated with the porosity of full saturated water (ΦF) and the porosity of movable water (ΦM). There is a negative correlation between ΦF and the seepage space fractal dimension (D S) in the coal samples with one-peak and two-peak T2 spectra, but a positive correlation can be found with the three-peak T2 spectrum. Therefore, it is necessary to consider the types of T2 spectral peak as a prerequisite to analyze the correlations between pore-fracture parameters and NMR fractal dimensions. With the increase of coal rank, the adsorption pore content, ΦF, and bulk volume immovable (BVI) fraction first increase and then decrease, whereas the seepage pore content, fracture development, bulk volume movable (BVM) fraction, and BVM/BVI first decrease and then increase. The inflection points of these changes correspond to the maximum vitrinite reflectance (R o,max) at 2.6-2.8%, which would be attributed to the third coalification jump. Generally, D A is the fractal dimension representing the coal pore surface, and D S and D M are closely related to the pore structure. Furthermore, D NMR not only represents the roughness of the pore surface but also the complexity of the pore structure.
The double pore (pores and fractures) structure in coals is not
only an important feature of reservoir structure, but also closely
related with the coalbed methane (CBM) storage and migration.[1,2] The quantitative characterization of the pore-fracture system is
of great significance to CBM exploration and development. The experimental
methods for characterizing the pore-fracture structure of coals mainly
include the following categories: (1) carbon dioxide (CO2) adsorption: it can effectively detect the micropores and ultra-micropores
smaller than 2 nm;[3] (2) low temperature
nitrogen(N2) adsorption: it can detect the distribution
and fractal characteristics of adsorption pores (pore size ≤100
nm) in coals;[4−6] and (3) mercury intrusion porosimetry: it can be
used to characterize the distribution and fractal characteristics
of pores (3.5 nm < pore size < 10 000 nm) by the relationship
between mercury injection pressure and pore size combined with classic
geometry models.[4,5,7] The
above three experiments belong to fluid intrusion detection methods,
which can partially destroy the coal structures. In addition, the
range of pore size in coals detected by each experiment is different;
therefore, the pore structure and fractal characteristics of coals
cannot be fully and accurately determined.[8,9] In
general, traditional methods have limitations in characterizing the
primariness and integrity of pore-fracture, but nuclear magnetic resonance
(NMR) with its speediness and non-destructive inspection can effectively
resolve these shortcomings.[10,11]The low-field
NMR can provide useful information about the pore-fracture
structure, porosity, and permeability parameters of coals, which has
the advantages of rapidity, accuracy, and high resolution in the analysis
of the physical properties of coal. In view of these advantages, this
method is widely used to study the pore/fracture size, shape, and
porosity of coals.[12−14] Coals with different coal ranks are characterized
by various pore structures, which can be expressed in different NMR
spectra.[15,16] Thus, it is a basis for analyzing the influence
of the metamorphic grade of coal on pore-fracture structure based
on NMR. The adsorption space fractal dimension (DA), seepage space fractal dimension (DS), fractal dimension of all effective transverse relaxation
time (T2) points under saturated water
(DNMR), and the free flow space fractal
dimension (DM) are calculated through
the relationship between the NMR T2 spectra
and the corresponding amplitude component.[4,17,18] Due to the comprehensive influences of the
bulk volume movable (BVM) and the bulk volume immovable (BVI), the
permeability in coals is positively correlated with BVM/BVI in seepage
pores, but negatively correlated with BVM/BVI in adsorption pores.[14] With the increase of DA, the adsorption capacity of coals is enhanced.[4]DS and DM decrease with increasing distribution areas of T2 > 2.5 ms and the sorting coefficient.[4]Previous studies have shown that the fractal
characterizations
of pore-fracture based on NMR can effectively reflect the heterogeneity
of coal reservoirs and quantitatively characterize the adsorption
and seepage capacity of coals.[4,17,19] However, there are few studies on the applicability evaluation of
the pore-fracture structure fractal characterizations using low-field
NMR experiments. In this study, the middle–high rank coal samples
were selected in typical coal mines and the different pore-fracture
fractal dimensions were calculated based on NMR. Besides, the variations
of pore-fracture structure parameters and coal material composition
were emphatically analyzed with the increase of coal rank, which can
further explain the influence of the coalification jump on pore-fracture
structure from a micro perspective.
Geological
Settings
The three areas concerned in this study cover the
Anhe, Jiaozuo,
and Huaibei coalfields in northern China (Figure ). The Carboniferous and Permian coal-bearing
strata in these areas are the object horizons. Anhe and Jiaozuo coalfields
are situated in the northwestern Henan province, which structurally
belong to the Taihang tectonic subregion in southern North China plate.
Among them, the no. 21 coal seam in the Permian Shanxi
Formation is widely developed, which is the main horizon of coal and
CBM exploration. The lithology of Shanxi Formation is mainly composed
of gray/dark-gray mudstone and sandy mudstone, coal, and carbonaceous
mudstone (Figure ).
The sedimentary environment was changed from deltaic plain in Anhe
coalfield to tidal-flat in Jiaozuo coalfield.[20,21] The metamorphic degree of no. 21 coal seam in Shanxi
Formation is transited from middle–high metamorphic coals (average Ro,max = 1.96%) in Anhe coalfield to high metamorphic
coals (average Ro,max = 2.88%) in Jiaozuo
coalfield.[20] The Huaibei coalfield is located
in northern Anhui province, and its coal-bearing stratum mainly includes
the Permian Shanxi Formation and Lower Shihezi Formation. Among them,
the thickness of Shanxi Formation ranges from 96 to 143 m, with the
lithology of gray/gray-white medium sandstone and siltstone, gray-black
mudstone, and coal seams (nos. 10 and 11). The thickness of Lower
Shihezi Formation is between 115 and 135 m. The lithology is mainly
light-grey medium sandstone, gray siltstone, dark gray sandy mudstone
and mudstone, and coal seams (nos. 6, 7, 8, and 9).[22] Tidal flat-lagoon is the dominant sedimentary environment
for Shanxi Formation and Lower Shihezi Formation in Huaibei coalfield.[23]
Figure 1
Location and coal-bearing stratum histogram of Anhe and
Jiaozuo
coalfields in Henan province and Huaibei coalfield in Anhui province
(A—location of Henan and Anhui provinces, B—location
of Anhe, Jiaozuo, and Huaibei coalfields, C—coal-bearing stratum
histogram of Anhe and Jiaozuo coalfields, and D—coal-bearing
stratum histogram of Huaibei coalfield).
Location and coal-bearing stratum histogram of Anhe and
Jiaozuo
coalfields in Henan province and Huaibei coalfield in Anhui province
(A—location of Henan and Anhui provinces, B—location
of Anhe, Jiaozuo, and Huaibei coalfields, C—coal-bearing stratum
histogram of Anhe and Jiaozuo coalfields, and D—coal-bearing
stratum histogram of Huaibei coalfield).
Sampling and Research Methods
Coal
Sampling
According to the distribution
of coal mines and CBM wells, a total of 21 coal samples were collected
from the underground working faces and CBM wells in Anhe, Jiaozuo,
and Huaibei coalfields (Table ). Among them, 6 samples were obtained from Anhe Coalfield,
11 from Jiaozuo coalfield, and 4 from Huaibei coalfield. The samples
of Anhe and Jiaozuo coalfields were taken from no. 21 coal
seam in the Permian Shanxi Formation. Besides, the samples of Huaibei
coalfield were taken from no. 8 coal seam in the Permian Low Shihezi
Formation. All the coal samples were well packed prior to performing
a series of experiments.
Table 1
Macroscopic Description,
Proximate
Analysis, Vitrinite Reflectance Measurement, and Maceral Observation
of Coal Samples in Anhe, Jiaozuo, and Huaibei Coalfieldsa
In order to better
characterize the physical properties of middle–high rank coals
in detail, the research methods and experiments in this paper consist
of the macroscopic description of coals, proximate analysis, vitrinite
reflectance measurement, coal maceral observation, methane (CH4) isothermal adsorption, NMR testing, and fractal theories
of pore-fracture.
Macroscopic Description
of Coal Samples
The macroscopic description of coal samples
is carried out according
to the China National Standard GB/T 18023-2000. Based on this standard,
the coal samples can be classified into four types including bright,
semi-bright, semi-dull, and dull coals, with the bright composition
at a proportion of >80, 50–80, 20–50, and <20%,
respectively.[5] The classification and determination
of macroscopic
description should be performed on the fresh and vertical section
of coal seam, coal core, or coal specimen. First, the coal sample
is divided into different layers according to the overall gloss intensity
and then the contents of bright composition are estimated layer by
layer to finally determine the macroscopic type of coal sample.
Proximate Analysis, Vitrinite Reflectance
Measurement, and Coal Maceral Observation
The proximate analysis
of coal samples is carried out according to China National Standard
GB/T 30732-2014, and the parameters are obtained from this testing
including the moisture content (Mad),
ash yield (Aad), volatile matter (Vad), and fixed carbon content (FCad). Mad and Aad can be acquired using the methods of air seasoning and rapid ashing,
respectively. The proximate analysis not only can understand the coal
quality characteristics but also is the basis for evaluating the pore
structure. According to the relevant results of proximate analysis,
the properties, types, processing effects, and the industrial utilization
of coals can be preliminarily evaluated.[24] The vitrinite reflectance measurement and maceral analysis (500
points) are performed based on China National Standards GB/T 6948-1998
and GB/T 8899-1998 under oil immersion in reflected light using a
Leitz MPV-3 photometer-based microscope. The volumes of vitrinite
(V), inertinite (I), and exinite (E) in coal samples can be obtained.[5,25]
Methane Isothermal Adsorption
Each
coal sample (90–120 g) was crushed and sieved to gain a particle
size ranging from 0.18 to 0.25 mm (60–80 mesh).[26] After the moisture equilibrium of each coal
sample was treated, the methane isothermal adsorption can be carried
out based on China National Standard GB/T 19560-2008. The Langmuir
volume (VL) and Langmuir pressure (PL) in equilibrium water condition can be determined
by an IS-100 high pressure isothermal adsorption apparatus at 30 °C
at a maximum equilibrium pressure of 10 MPa.[2]
Nuclear Magnetic Resonance
NMR
measurements were performed by using a MesoMR23-60H-I medium size
NMR analyzer following the Industrial Standard of SY/T 6490-2007.
Several parameters were set with a resonance frequency of 23.406 MHz,
magnet strength of 0.5 T, coil diameter of 25 mm, magnet temperature
of 32 ± 0.02 °C, waiting time (TW) of 1500 ms, scanning
numbers of 64, and echo spacing (NECH) of 3000. First, the samples
were vacuumed for 5 h and injected with distilled water. Then, they
were filled with water for 24 h under a pressure of 10 Pa. Moreover,
all the samples were subjected to low-field NMR experiments with 100%
water saturation to obtain the T2 spectrum.
Next, they were put into the centrifuge at a speed of 8000 rpm to
make sure that the weights of samples were no longer reduced. All
the coal samples were subjected to low-field NMR experiments again
to obtain the T2 spectrum under bound
water.[27] Both the coal porosity and permeability
were measured using the NMR geometric mean T2 and producible porosity models, respectively.[4]
Fractal Theory of Pore-Fracture
with NMR
DA, DS, DNMR, and DM are
calculated by NMR results. Among them, DA, DS, and DNMR are the fractal dimensions under saturated water, and DM is the fractal dimension of pore-fracture space fluid
under the combination condition of saturated water and bound water.[14]DA (T2 < 2.5 ms), DS (T2 > 2.5 ms), and DNMR can be calculated from eqs and 2, and DM can be calculated from eqs and 4.where W is the percentage
of pore accumulate volume in the total pore volume when transverse
relaxation time is less than T2, T2 is the transverse relaxation time, and T2max is the maximum transverse relaxation time.[4]Vw and Vir are the cumulative amplitudes of the NMR T2 spectrum under saturated and bound water, respectively.[14]K is a constant. Through eq , we describe a forceful
linear relationship between lg(W) and lg(T2), from which DA, DS, and DNMR can be obtained. Through eq , we describe another forceful linear relationship between
lg(V) and lg(T2), from
which DM can be calculated.
Results
Coal Petrology and Proximate
Analysis
The results of macroscopic description, vitrinite
reflectance, proximate
analysis, and maceral observation of coal samples are shown in Table . Among the 21 coal
samples, most of them are semi-bright and semi-dull coals, with only
a small amount of bright coals. The ranges of V, I, and E contents
of the coal samples are 62.06–98.22% (84.62% on average), 1.78–37.94%
(12.82% on average), and 0–9.14% (2.37% on average), respectively
(Table ). Therefore,
the macerals of middle–high rank coals in this study region
are dominated by V, followed by I, and the contents of E are the lowest. Ro,max of the coal samples ranges from 1.08 to
3.32%, with an average of 2.36%. Among them, Ro,max of Jiaozuo coalfield is between 2.45 and 3.32% (2.88%
on average), with that of Anhe coalfield ranging from 1.27 to 2.32%
(1.96% on average), and that of Huaibei coalfield ranging from 1.08
to 2.12% (1.53% on average), indicating that Jiaozuo coalfield belongs
to high metamorphic anthracite, and Anhe and Huaibei coalfields belong
to middle–high metamorphic coals.Mad of all the samples is in the range from 0.54 to 3.69% with
an average value of 1.54% (Table ), which suggests that all the samples belong to low
moisture coals. Among them, the ranges of Mad in Jiaozuo, Anhe, and Huaibei coalfields are 1.06–3.69% (1.75%
on average), 0.84–2.88% (1.71% on average), and 0.54–0.99%
(0.69% on average), respectively. The moisture content in coals has
an increasing trend with the rise of metamorphic grade (Figure a) and Ro,max corresponding to the lowest moisture content is 1.08%
(Wugou coal mine). At this point, the dehydration process has been
completed, and the content of structural water in coals increases
gradually with the increase of coal rank.[28] It should be noted that a jump change is found at 2.6–2.8%
of Ro,max (Figure a), which might be attributed to the third
coalification transition. Previous studies show that when Ro,max is less than 1.1%, the coals are mainly
filled with free water, and the moisture content decreases with increasing
coal rank.[28] When Ro,max is greater than 1.1%, the coals are mainly filled with
structural water, and the moisture content increases gradually with
the augment of coal rank. Therefore, the changes of moisture content
in coals are closely related to coal rank.
Figure 2
Variation characteristics
of Mad, Aad, Vad, and FCad with coal
rank of coal samples in Anhe, Jiaozuo, and Huaibei
coalfields. (a) Mad vs. Ro,max. (b) Aad vs. Ro,max. (c) Vad vs. Ro,max. (d) FCad vs. Ro,max.
Variation characteristics
of Mad, Aad, Vad, and FCad with coal
rank of coal samples in Anhe, Jiaozuo, and Huaibei
coalfields. (a) Mad vs. Ro,max. (b) Aad vs. Ro,max. (c) Vad vs. Ro,max. (d) FCad vs. Ro,max.Aad of all the samples under air-dried
basis is between 5.76 and 15.13% with an average of 10.22% (Table ), indicating that
all the samples belong to low-medium ash coals. Specifically, the
ranges of Aad in Jiaozuo, Anhe, and Huaibei
coals are 6.43–14.49% (9.16% on average), 6.34–15.13%
(11.66% on average), and 5.76–14.40% (10.97% on average), respectively.
The ash in coals mainly comes from the terrigenous clastic filling
and groundwater circulation in peat swamps, which has little relationship
with the metamorphic grade of coals (Figure b). Vad of all
the samples varies from 5.28 to 28.78%, with an average value of 10.75%
(Table ). Among them,
the ranges of Vad in Jiaozuo, Anhe, and
Huaibei coals are 5.28–8.02% (6.14% on average), 6.45–21.33%
(13.25% on average), and 8.18–28.78% (19.65% on average), respectively. Vad is closely related to the metamorphic degree
of coals, which shows a negative correlation between them (Figure c). FCad of all the samples is within a range from 56.87 to 86.75%, with
an average of 77.50% (Table ). Among them, the ranges of FCad in Jiaozuo, Anhe,
and Huaibei coals are 75.69–86.75% (82.94% on average), 65.68–80.39%
(73.39% on average), and 56.87–80.94% (68.69% on average),
respectively. FCad can reflect the metamorphic degree of
coals to a certain extent,[29] so it has
a good linear positive correlation with Ro,max(Figure d).
Isothermal Adsorption Experiment of Methane
Based on
the methane isothermal adsorption experiment, both VL and PL of the
eight coal samples were measured (Table ). The eight samples were collected from
no. 1 of Zhaogu coal mine (ZG-1), no. 2 of Zhaogu coal mine (ZG-2),
Anlin coal mine (AL), no. 9 of Hebi coal mine (HB-9), no. 6 of Hebi
coal mine (HB-6), Gubei coal mine (GB), Haizi coal mine (HZ), and
Yuanzhuang coal mine (YZ). The physical meaning of VL is the maximum volume of methane in coals. The experimental
results show that VL ranges from 14.52
to 33.87 mL/g, with an average of 24.14 mL/g. PL is between 1.94 and 3.5 MPa with an average of 2.71 MPa.
In addition, the methane adsorption capacity of ZG-2 in Jiaozuo coalfield
is the strongest with VL of 33.87 mL/g,
whereas that of GB in Huaibei coalfield is the weakest with VL of 14.52 mL/g.
Table 2
Parameters
of NMR Experiments and
Methane Isothermal Adsorption of Coal Samples in Anhe, Jiaozuo, and
Huaibei Coalfieldsa
sample no.
types of T2 spectral
peaks
porosity
of full saturated water (%)
permeability
(mD)
T2 cutoff value (ms)
BVI (%)
BVM (%)
BVM/BVI
porosity
of movable water (%)
VL (mL/g)
PL (MPa)
2403-2
two-peak
6.94
0.0882
2.6
91.02
8.98
0.09866
0.625
2403-4
two-peak
5.73
0.0047
2.91
96.77
3.23
0.033378
0.156
4001-1
two-peak
5.95
0.1321
2.12
85.89
14.11
0.16428
0.594
11601-1
two-peak
8.96
0.3925
3.35
88.9
11.1
0.124859
1.11
11601-2
two-peak
7.53
0.2582
2.02
87.46
12.54
0.14338
1.03
7601-2
two-peak
5.51
0.2
1.42
80.9
19.1
0.236094
1.01
7601-3
two-peak
5.63
0.037
1.65
91.2
8.8
0.096491
0.68
7601-6
two-peak
5.33
0.053
1.46
88.56
11.44
0.129178
0.82
7601-9
two-peak
7.48
0.21
2.12
88.42
11.58
0.130966
1.27
ZG-1
one-peak
6.89
0.0024
3.04
98.36
1.64
0.016673
0.15
32.12
3.12
ZG-2
one-peak
8.68
0.17
3.27
91.98
8.02
0.087193
1.01
33.87
3.5
LS
one-peak
5.69
0.032
1.44
91.83
8.17
0.088969
0.67
DZ
three-peak
3.3
0.0038
0.99
91.66
8.34
0.090988
0.23
ZJ
three-peak
1.01
0.025
7.71
28.55
71.45
2.502627
0.73
AL
three-peak
4.35
0.19
0.97
73.26
26.74
0.365001
1.14
25.75
2.22
HB-9
three-peak
2.67
0.034
0.52
70.83
29.17
0.411831
0.83
21.59
1.95
HB-6
three-peak
3.2
0.68
0.33
43.67
56.33
1.289902
1.92
22.6
1.94
GB
three-peak
2.04
0.49
0.32
27.14
72.86
2.684598
1.49
14.52
2.9
HZ
three-peak
0.63
0.13
0.4
6.46
93.54
14.47988
0.59
17.65
3.43
WG
three-peak
2.23
8.31
0.31
9.73
90.27
9.277492
2.02
YZ
two-peak
1.08
0.00005
0.65
91.2
8.8
0.096491
0.11
25.03
2.6
/, no data.
/, no data.It is found that VL increases with
increasing Ro,max values, and the correlation
coefficient (R2) is 0.9486 (Figure a), which suggests that the
coal rank has a dominant control on the adsorption capacity. Previous
investigations show that large pores gradually decrease, whereas small
pores and micropores gradually increase with the increase of coal
rank. Plenty of small pores and micropores provide more adsorption
spaces for methane adsorption, thus enhancing the adsorption capacity
of coals.[28] The physical meaning of PL is the pressure when the actual adsorption
capacity of methane reaches 50% of the maximum adsorption capacity,
which reflects the difficulty degree of CBM desorption and has little
relationship with the metamorphic degree of coals (Figure b).
Figure 3
Correlations of VL, PL, and coal
rank of coal samples in Anhe, Jiaozuo, and
Huaibei coalfields. (a) VL vs. Ro,max. (b) PL vs. Ro,max.
Correlations of VL, PL, and coal
rank of coal samples in Anhe, Jiaozuo, and
Huaibei coalfields. (a) VL vs. Ro,max. (b) PL vs. Ro,max.
Parameter Analysis of NMR Experiment
There
are three types of NMR T2 spectra
of the coal samples under saturated water including one-peak, two-peak,
and three-peak (Figure ), which mainly represent the adsorption pores, adsorption and seepage
pores, whole pores and fractures, respectively. Specifically, the
peak of NMR T2 spectrum of the adsorption
pores (micropores and small pores) is located at 0.5–2.5 ms,
the seepage pores (medium-large pores) at 2.5–50 ms, and the
fractures at >100 ms.[10]
Figure 4
Types of NMR T2 spectra in Anhe, Jiaozuo,
and Huaibei coals (a, one-peak; b, two-peak; and c,d, three-peak).
Types of NMR T2 spectra in Anhe, Jiaozuo,
and Huaibei coals (a, one-peak; b, two-peak; and c,d, three-peak).Taking the Wugou coal sample as an example (Figure d), it can be said
that: (1) the three spectrum
peaks of this sample reflect three pore-fracture types, respectively,
among which the spectrum peak of medium-large pores is higher and
wider, indicating that the medium-large pores are the most developed;
(2) the spectrum peak of the micropores and small pores is lower,
and the change of spectrum form is the smallest after centrifugation,
showing that the micropores and small pores are moderately developed
with poor connectivity; (3) most of the spectrum peak of the medium-large
pores disappear after centrifugation, suggesting that the medium-large
pores have a better connectivity; (4) the spectrum peak of the fractures
basically disappears after centrifugation, illustrating that the connectivity
of fractures is the best; and (5) before centrifugation, the T2 spectra of the micropores, small pores, and
medium-large pores, as well as medium-large pores and fractures are
continuous, indicating that there are certain connectivities among
them.Several parameters including the porosity of full saturated
water
(ΦF), permeability, BVI, BVM, and porosity of movable
water (ΦM) in coal samples were measured by NMR experiments
(Table ). ΦF of Jiaozuo, Anhe, and Huaibei coals ranges from 5.33 to 8.96%
(6.78% on average), from 1.01 to 5.69% (3.37% on average), and from
0.63 to 2.23% (1.50% on average), respectively. The coal porosities
in the three coalfields are quite different, among which Jiaozuo coals
are the highest, whereas Huaibei coals are the lowest. The permeabilities
of the Jiaozuo, Anhe, and Huaibei coals range from 0.0024 to 0.3925
mD (0.14 mD on average), from 0.0038 to 0.68 mD (0.16 mD on average),
and from 0.00005 to 8.31 mD (2.23 mD on average), respectively. BVI
of all samples is in the range from 6.46 to 98.36% with an average
value of 72.56%, and the range of BVM is 1.64–93.54% with an
average value of 27.44%. ΦM of all the samples is
within a range from 0.11 to 2.02% (0.87% on average) with the greatest
value in the Huaibei coals, followed by the Anhe and Jiaozuo coals.
Fractal Dimensions of Pore-Fracture Based
on NMR Experiments
The pore-fracture fractal dimensions including DA, DS, DNMR, and DM can be obtained
by the results of NMR experiments and the previous calculation formulas
(Table ). DA values of the Jiaozuo, Anhe, and Huaibei coals
range from −0.1047 to 1.3368 (0.7169 on average), from 0.1816
to 1.5377 (1.1456 on average), and from 0.3279 to 1.7107 (1.3157 on
average), respectively. DS values of the
Jiaozuo, Anhe, and Huaibei coals are between 2.6856 and 2.9932 (2.9410
on average), 2.7698 and 2.9938 (2.9298 on average), along with 2.5821
and 2.9949 (2.8091 on average), respectively. DNMR values of the Jiaozuo, Anhe, and Huaibei coals vary from
2.4679 to 2.8288 (2.6820 on average), from 2.3128 to 2.7996 (2.6661
on average), and from 2.2996 to 2.8069 (2.6219 on average), respectively. DM values of the Jiaozuo, Anhe, and Huaibei coals
are in the ranges from 2.0103 to 3.4350 (2.6665 on average), from
2.4680 to 3.7142 (3.2403 on average), and from 2.6728 to 3.7433 (3.3115
on average), respectively.
Table 3
Pore-Fracture Fractal
Dimensions and
Fitting Degree Based on NMR Experiments (DA, T2 < 2.5 ms under Saturated Water; DS, T2 > 2.5 ms
under
Saturated Water; DNMR, All Effective T2 Points under Saturated Water; and DM, Centrifugation/Saturated Water)
sample no.
3-DA
DA
RA2
3-DS
DS
RS2
3-DNMR
DNMR
RNMR2
DM-3
DM
RM2
2403-2
2.4704
0.5296
0.9117
0.0129
2.9871
0.9709
0.4945
2.5055
0.4929
–0.2668
2.7332
0.6136
2403-4
2.4049
0.5951
0.9146
0.0095
2.9905
0.9794
0.5321
2.4679
0.5114
–0.9897
2.0103
0.7073
4001-1
2.1355
0.8645
0.891
0.0167
2.9833
0.9831
0.4837
2.5163
0.5068
–0.1811
2.8189
0.9667
11601-1
2.6009
0.3991
0.8794
0.0361
2.9639
0.9825
0.2721
2.7279
0.3802
–0.3236
2.6764
0.5921
11601-2
2.2333
0.7667
0.8996
0.0164
2.9836
0.9845
0.5122
2.4878
0.5152
–0.2357
2.7643
0.9805
7601-2
1.8517
1.1483
0.8112
0.0068
2.9932
0.8044
0.2001
2.7999
0.3315
–0.7575
2.2425
0.6172
7601-3
1.6632
1.3368
0.813
0.0147
2.9853
0.8502
0.2027
2.7973
0.3553
0.1401
3.1401
0.3198
7601-6
1.8034
1.1966
0.8282
0.0139
2.9861
0.9758
0.1944
2.8056
0.3326
–0.7106
2.2894
0.6846
7601-9
2.5998
0.4002
0.7695
0.0268
2.9732
0.9826
0.2234
2.7766
0.2982
0.435
3.435
0.685
ZG-1
2.246
0.754
0.8726
0.1808
2.8192
0.9466
0.1712
2.8288
0.3071
–0.9735
2.0265
0.7836
ZG-2
3.1047
–0.1047
0.8345
0.3144
2.6856
0.9026
0.2116
2.7884
0.301
0.1951
3.1951
0.1708
LS
1.8298
1.1702
0.7716
0.0062
2.9938
0.9497
0.2004
2.7996
0.3132
0.398
3.398
0.6327
DZ
1.7523
1.2477
0.7707
0.0117
2.9883
0.9745
0.3103
2.6897
0.3736
0.7037
3.7037
0.6772
ZJ
2.8184
0.1816
0.8152
0.2302
2.7698
0.9628
0.6872
2.3128
0.5551
0.7142
3.7142
0.9554
AL
1.4623
1.5377
0.7995
0.0412
2.9588
0.932
0.2114
2.7886
0.3883
–0.0523
2.9477
0.6877
HB-9
1.4989
1.5011
0.7156
0.0369
2.9631
0.9857
0.2344
2.7656
0.3455
0.2099
3.2099
0.4782
HB-6
1.7645
1.2355
0.745
0.0951
2.9049
0.9881
0.3599
2.6401
0.4324
–0.532
2.468
0.6002
GB
1.4741
1.5259
0.7438
0.1149
2.8851
0.8605
0.3198
2.6802
0.4992
0.4878
3.4878
0.5616
HZ
2.6721
0.3279
0.7856
0.4179
2.5821
0.9778
0.7004
2.2996
0.5933
0.342
3.342
0.3394
WG
1.3016
1.6984
0.7348
0.2258
2.7742
0.8145
0.2991
2.7009
0.6145
–0.3272
2.6728
0.9206
YZ
1.2893
1.7107
0.7124
0.0051
2.9949
0.9732
0.1931
2.8069
0.3258
0.7433
3.7433
0.3774
In general, DA of all
the coal samples
is between −0.5 and 2, and DM varies
from 2 to 4. Besides, both DS and DNMR range from 2 to 3 (Figure ). Fractal theories reflect the surface and
morphological characteristics of pore fracture in coals, with the
complex surface and morphology usually corresponding to high fractal
dimensions.[14] In addition, DS is significantly larger than DA, indicating that the structure of seepage pores in coals
is more complex than that of adsorption pores. DNMR is between DA and DS because it is the fractal dimension covering the adsorption
and seepage pores. DM varies greatly with
increasing Ro,max, which would be related
to the proportion of free water layer and bound water layer existing
in the pore-fracture space of coal samples.[30]
Figure 5
Variation
features of DA, DS, DNMR, and DM with coal rank of coal samples in Anhe, Jiaozuo, and
Huaibei coalfields.
Variation
features of DA, DS, DNMR, and DM with coal rank of coal samples in Anhe, Jiaozuo, and
Huaibei coalfields.
Discussion
Relationships between Fractal Dimensions of
NMR Pore-Fracture and Methane Adsorption Capacity
DA is positively correlated with VL of the coal samples on the condition of three-peak T2 spectrum (Tables and 3). The methane
adsorption data of coal samples are relatively few with one-peak (2
samples) and two-peak (1 sample) T2 spectra,
thus it is not further discussed. DNMR is also positively correlated with VL (Figure a), which
shows that (1) both DA and DNMR represent the fractal dimensions of the coal pore
surface because VL is controlled by the
pore surface area;[31] (2) the methane adsorption
capacity of coals is not only related to the surface roughness of
adsorption pores but also to the pore surface area of the whole aperture
section, and the larger the DA and DNMR are, the rougher the surface of coal particles
is and the stronger the adsorption capacity of coals is;[4,32] and (3) it is necessary to consider different types of T2 spectrum when analyzing the relationship between DA and VL.
Figure 6
Relationships
between VL, DNMR, and adsorption pore proportion (in volume) of coal
samples in Anhe, Jiaozuo, and Huaibei coalfields. (a) VL vs. DNMR. (b) VL vs. adsorption pore volume percentage.
Relationships
between VL, DNMR, and adsorption pore proportion (in volume) of coal
samples in Anhe, Jiaozuo, and Huaibei coalfields. (a) VL vs. DNMR. (b) VL vs. adsorption pore volume percentage.Compared with seepage pores, the proportion and specific
surface
area of adsorption pores are more closely related to the methane adsorption
capacity. Specifically, VL is positively
correlated with the volume proportion of adsorption pores (Figure b). The contents
of micropores and small pores gradually increase with increasing volume
proportion of adsorption pores, providing more adsorption spaces for
methane, which enhances the adsorption capacity and VL values of coals.[2] In addition,
the larger the volume proportion of adsorption pores is, the more
uneven the pore distribution is, resulting in a more complex pore
structure and larger DNMR. Therefore,
the coals with complex pore structure usually have high adsorption
capacity of methane, which is beneficial to the adsorption of CBM,
but not conducive to desorption and the seepage of CBM.[4,33] If the NMR experiment was performed with filling CH4 in
coals, the significant swelling amount could result in the changes
of coal porosity and permeability, which significantly determines
the pore surface area and pore size distribution.[34]
Influences of NMR Fractal
Dimensions on Porosity
and Permeability
DS has some
internal relationships with ΦF of the coal samples
(Figure a), but it
is worth noting that the trends between DS and ΦF are different with different T2 spectral peaks. Specifically, DS is negatively correlated with ΦF of the
coals under one-peak and two-peak T2 spectra;
however, DS is positively correlated with
ΦF under the three-peak T2 spectrum. This indicates that DS can
reflect the pore structure characteristics of coals, and it is necessary
to take the T2 spectral peak type as a
prerequisite for the analysis of pore-fracture through DS (Figure a).[32] When the T2 spectra are one-peak or two-peak, the changes of porosity
are mainly controlled by the volume proportions of various pores due
to less-developed fractures and poor pore connectivity. Thus, the
more complex the pore structure is, the lower the porosity is, which
is consistent with the previous research results.[33] When the T2 spectrum is three-peak,
the changes of porosity might be related to the complexity of pore
shape as the pore connectivity is good and the volume proportion of
each pore section is relatively balance-distributed. Besides, when
the T2 spectra are one-peak and two-peak,
the porosity of coals is greatly influenced by the various pore volume
proportions and connectivities. When the T2 spectrum is three-peak, the morphological complexity of pores might
play a major role in controlling the porosity of coals.
Figure 7
Relationships
between NMR fractal dimensions and porosity/permeability
parameters (a, b—ΦF vs. DS, DM; c—ΦM vs. DM; and d—permeability
vs. ΦM) of coal samples in Anhe, Jiaozuo, and Huaibei
coalfields.
Relationships
between NMR fractal dimensions and porosity/permeability
parameters (a, b—ΦF vs. DS, DM; c—ΦM vs. DM; and d—permeability
vs. ΦM) of coal samples in Anhe, Jiaozuo, and Huaibei
coalfields.In order to analyze the physical
meaning represented by DM, the internal
relationships between DM and ΦF, ΦM of coals are analyzed (Figure b,c). The results show that DM is inversely proportional to ΦF when DM is divided into two parts by
2.675 (Figure b),
which means that
the negative correlation would be stronger in a certain DM range. Besides, DM is negatively
correlated with ΦM of coal samples (Figure c), but this negative correlation
would be more obvious if the T2 spectra
are classified based on different types. Generally, DM is negatively correlated with ΦF and
ΦM, indicating that DM represents the fractal dimension of the coal pore structure, which
is generally consistent with the results of previous studies.[4] However, the classifications of DM and T2 spectrum are not
considered in previous studies. In this study, when analyzing the
porosity and permeability of coals through DM, it is necessary to refer to the distribution characteristics
of the NMR T2 spectrum to establish a
prediction model applicable to different T2 spectrum distributions. This is because the different T2 spectra generally determine the volume proportions of
various pores and fractures, on which basis the fractal characterizations
of the pore-fracture structure will be more statistically significant.There is an obvious positive correlation between ΦM and permeability (Figure d), which suggests that the samples with high porosity also
have high permeability. The porosity of coals is composed of the pore
space with relatively poor connectivity and the free space volume
occupied by the fractures with good connectivity. Although the pore
space occupied by coal fractures is limited, it is the main channel
of CBM seepage.[28] In general, the coals
with higher ΦM usually correspond to more proportion
of fractures and stronger permeability (Figure d). Both DS and DM are related to the porosity of coals (Figure a–c), and
the porosity is significantly positively correlated with the permeability
(Figure d). Therefore, DS and DM are also
related to the permeability,[35,36] which indicates that DS and DM are fractal
dimensions characterizing the pore structure of coals.
Relationships between NMR Fractal Dimensions
and Pore-Fracture Volume
The volumes of adsorption pores
(T2 < 2.5 ms), seepage pores (2.5 ms
< T2 < 50 ms), and fractures (T2 > 100 ms) of coals can be calculated based
on the NMR T2 spectrum distribution under
saturated water.[9] The correlation analyses
are performed between the volume percentages of adsorption pores,
seepage pores, fractures of coal samples, and DNMR (Figure ). The results show that DNMR is positively
correlated with the volume proportion of adsorption pores (Figure a), whereas there
are negative relationships between DNMR and the volume proportions of seepage pores and fractures (Figure b,c). It indicates
that the coal samples with high DNMR have
more adsorption pores and less seepage pores and fractures. Due to
larger adsorption pores proportion, coals usually have rougher pore
surface and greater specific surface area, which results in a bigger DNMR (Figure a). The coals with great volume proportions of seepage
pores and fractures have good pore connectivity and high permeability,
which corresponds to a simple pore structure and a small DNMR (Figure b,c). Therefore, DNMR can not only reflect
the roughness of coal pore surface but also represent the complexity
of coal pore structure to some extent. Generally, the coals with high DNMR usually have a rough pore surface and can
adsorb more methane. However, the complex pore structure with poor
porosity and permeability is not conducive to desorption and the seepage
of methane.[33]
Figure 8
Relationships between DNMR and the
volume proportions of adsorption pores, seepage pores, and fractures
in Anhe, Jiaozuo, and Huaibei coalfields. (a) Adsorption pore volume
percentage vs. DNMR. (b) Seepage pore
volume percentage vs. DNMR. (c) Fracture
volume percentage vs. DNMR.
Relationships between DNMR and the
volume proportions of adsorption pores, seepage pores, and fractures
in Anhe, Jiaozuo, and Huaibei coalfields. (a) Adsorption pore volume
percentage vs. DNMR. (b) Seepage pore
volume percentage vs. DNMR. (c) Fracture
volume percentage vs. DNMR.
Pore-Fracture Structure Evolution with the
Coalification Process
Variation Characteristics
of Different Pore-Fractures
in Coals with Coal Rank
The relationships between coal rank
and volume proportions of adsorption pores, seepage pores, and fractures
are shown in Figure . The results indicate that with the increase of Ro,max, the volume proportion of adsorption pores in coals
increases first and then decreases (Figure a). Meanwhile, the volume proportions of
seepage pores and fractures rapidly decrease first and then increase
slowly (Figure b,c).
It should be noted that the inflection points of these changes correspond
to Ro,max at 2.6–2.8%, which would
be closely related with the coalification jump. Almost all the oxygen-containing
functional groups fall off and the aromatic rings gradually add with
orderly molecular arrangement in coals between the second and third
coalification jumps.[28]
Figure 9
Volume proportions of
adsorption pores, seepage pores, and fractures
with coal rank in Anhe, Jiaozuo, and Huaibei coals. (a) Adsorption
pore volume percentage vs. Ro,max. (b)
Seepage pore volume percentage vs. Ro,max. (c) Fracture volume percentage vs. Ro,max.
Volume proportions of
adsorption pores, seepage pores, and fractures
with coal rank in Anhe, Jiaozuo, and Huaibei coals. (a) Adsorption
pore volume percentage vs. Ro,max. (b)
Seepage pore volume percentage vs. Ro,max. (c) Fracture volume percentage vs. Ro,max.In this process, the volume proportion
of adsorption pores is predominant
in the pore system, whereas the content of seepage pores gradually
reduces, which leads to a worse pore connectivity and a decrease of
fracture development. As the augmenter of adsorption pores is higher
than the decrease of seepage pores and fractures,[28] the porosity increases continually with increasing coal
rank (1.1% < Ro,max < 2.8%) before
the inflection point (Figure a). Although the volume of seepage pores and fractures increase
after this inflection point, the augmenter is less than the decrement
of adsorption pores, which results in a slow decline with the increase
of coal rank (Figure a).
Figure 10
Variation characteristics of ΦF, T2 cutoff value, BVI, BVM, BVM/BVI, and ΦM with coal rank in Anhe, Jiaozuo, and Huaibei coals (the red dot
in Figure b is the
outlier). (a) ΦF vs. Ro,max. (b) T2 cutoff value vs. Ro,max. (c) BVI vs. Ro,max.
(d) BVM vs. Ro,max. (e) BVM/BVI vs. Ro,max. (f) ΦM vs. Ro,max.
Variation characteristics of ΦF, T2 cutoff value, BVI, BVM, BVM/BVI, and ΦM with coal rank in Anhe, Jiaozuo, and Huaibei coals (the red dot
in Figure b is the
outlier). (a) ΦF vs. Ro,max. (b) T2 cutoff value vs. Ro,max. (c) BVI vs. Ro,max.
(d) BVM vs. Ro,max. (e) BVM/BVI vs. Ro,max. (f) ΦM vs. Ro,max.
Variation
Characteristics of NMR Parameters
with Coal Rank
The variation characteristics of ΦF, T2 cutoff value, BVI, BVM, BVM/BVI,
and ΦM of coal samples with the increase of coal
rank are shown in Figure . The results show that, with the increase of coal rank, ΦF first increases and then decreases slightly, and it becomes
discrete with Ro,max at 2.6–2.8%
(Figure a). The
variation of coal porosity is essentially controlled by the distributions
of adsorption pores, seepage pores, and fracture volume (Figure ). The T2 cutoff value is the boundary value between BVM and BVI.
It is generally considered that the fluid larger than the T2 cutoff value on the T2 spectrum is BVM, whereas the fluid smaller than the T2 cutoff value is BVI.[28] With the increase of coal rank, the T2 cutoff value increases continuously, and the maximum value can reach
3.35 ms (Figure b). It is worth noting that there is an abnormal point (ZJ in Anhe
coalfield) with the porosity component of adsorption pores after centrifugation
higher than that before centrifugation (Figure c), which would be caused by the experimental
settings. Due to the complexity of the pore-fracture structure, the T2 cutoff value cannot directly reflect the levels
of porosity and permeability.[12,28] In general, the coals
with a higher T2 cutoff value mean that
they have more bound fluids (Figure b,c). With the augment of coal rank, the bound fluid
content increases rapidly first and then reduces slowly (Figure c), whereas the
movable fluid content decreases rapidly first and then adds slowly
(Figure d). The
changes of bound fluid in coals are consistent with the variation
of adsorption pore content (Figure a). Because the bound water is mainly stored in the
adsorption pores,[37] when Ro,max is less than 2.8%, the content of adsorption pores
and the bound fluid add with the increase of Ro,max. When Ro,max is greater than
2.8%, the content of adsorption pores reaches the maximum and then
decreases slightly (Figure a), and so does the content of bound fluid (Figure c).With the increase
of coal rank, BVM first reduces and then adds slightly, but the variation
trend of BVI is opposite (Figure c,d). It is accepted that the movable water is mainly
stored in the seepage pores.[37] When Ro,max is less than 2.8%, the content of seepage
pores decreases with the increase of Ro,max (Figure b), and
the content of movable water reduces at the same time (Figure d). When Ro,max is greater than 2.8%, the content of seepage pores
increases slightly after reaching the minimum (Figure b), and so does the content of movable water
(Figure d). In addition,
the variation trend of BVM is generally consistent with ΦM (Figure d,f). The larger the ΦM, the greater the BVM and
higher the permeability (Figure d).[38] BVM/BVI can be used
to characterize the connectivity and permeability of pore-fracture.[14,28] The larger the BVM/BVI, the better the connectivity and permeability.[39] In this study, BVM/BVI decreases with the increase
of coal rank, and it increases slightly after reaching the minimum
value (Figure e). Ro,max corresponding to the inflection point
of this change is about 2.8%. Therefore, coals in the medium metamorphic
grade (1.1% < Ro,max < 1.5%) have
high connectivity, permeability, and BVM/BVI due to the relatively
developed endogenous fractures.[40] ΦM decreases with the increase of coal rank, which is consistent
with the changes of BVM/BVI (Figure e,f). However, the correlation coefficient of ΦM with Ro,max is low, which would
be related to the variation characteristics of ΦM under different NMR T2 spectra (Figure f).
Conclusions
DA is
the fractal dimension representing the coal pore surface, and DS, DM are the fractal
dimensions reflecting the pore structure. DNMR can not only reflect the roughness of pore surface but also characterize
the complexity of pore structure of coals.ΦF and ΦM are
negatively correlated with DM, but it
is necessary to consider the T2 spectral
peak types as a precondition. Under the condition of one-peak
and two-peak T2 spectra, there is a negative
correlation between ΦF and DS, whereas under the condition of three-peak T2 spectrum, ΦF is positively correlated
with DS.With the increase of coal rank, the
adsorption pore content, ΦF, and BVI first increase
and then decrease, whereas the seepage pore content, the fracture
development, BVM, and BVM/BVI first reduce and then increase. The
inflection points of these changes correspond to Ro,max at 2.6–2.8%. In addition, the moisture content
also shows a jump change with Ro,max at
2.6–2.8%, which might be related to the third coalification
jump.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10