Experimental Investigation of Pore Characteristics and Permeability in Coal-Measure Sandstones in Jixi Basin, China

Abstract

The research of pore and permeability characteristics of tight sandstone reservoirs in coal-measure is critical for coal-measure gas development. In this study, the pore systems of tight sandstones were studied based on low-field nuclear magnetic resonance (LF-NMR) data. The permeability of tight sandstones was obtained by the tester based on the pulse transient method. The permeability variation with the effective stress, grains, and pore characteristics was analyzed. The results show that the tight sandstone reservoirs in the coal-measure have low total porosity (2.80–4.14%), low effective porosity (0.51–1.56%), and low permeability (0.351 × 10⁻⁶–13.910 × 10⁻⁶ um²). LF-NMR T₂ spectra of the testing sandstones show that the micropores are the most developed, but most of the micropores are immovable pores. The pore characteristics are significantly affected by the grain size of sandstones. The pore connectivity ranks from good to poor with decreasing sandstone particle size. The total porosity and effective porosity increase with the grain size. There is a near-linear negative relationship between permeability and effective stress when the effective stress is between 405 psi and 808 psi. The greater the number of movable pores and the larger the effective porosity, the bigger the permeability of the sandstone. The effective porosity of sandstones is a sensitive indicator for evaluating the permeability of tight sandstone reservoirs. The stress sensitivity coefficient of permeability (S_s) increases with the increase of the effective stress. The sandstone with lower permeability, smaller effective porosity, and finer grains has a higher S_s. The particle size of sandstone from coal-measure has a great influence on both permeability and S_s. The findings will provide a better understanding of the characterization of pore structure and permeability in the process the coal-measure gas extraction, which is useful for the efficient development of coal-measure gas.

1. Introduction

The coal-measure formation is rich in unconventional natural gas resources, which is called coal-measure gas, including coalbed methane in coal reservoirs, tight sandstone gas in sandstone reservoirs, and shale gas in shale reservoirs [1,2]. Coal-measure gas development has attracted global attention because of its huge resource potential, especially in China [1,3,4]. Coal seams are generally mixed with sandstones, mudstones, and shales in coal-measure [5]. Coal seams and shale in the coal-measure could be the main source rocks for coal-measure gas because they are favorable for hydrocarbon generation and gas accumulation, while the conditions, such as burial depth, time, and temperature, are appropriate [1,6,7]. Sandstones in the coal-measure are one kind of reservoir that could store gas charged by the above source rocks [4,6,8,9]. Most of the sandstones in coal-measure are tight sandstones because their porosity is less than 10%, and their permeability is less than 0.1 mD [1,6,10]. The reservoir characteristics among the coal, shale, and sandstone in the coal-measure vary greatly [11]. The pore and permeability characteristics of the coal-measure gas reservoir could affect the gas accumulation and production [12,13]. Many studies have focused on the reservoir characteristics of coal [14,15], while the research on the pore and permeability characteristics of tight sandstone in coal-measure in the study area has been less focused upon. The tight sandstones in coal-measure are characterized by smaller pores and complex pore throat connections [16], which lead to lower permeability. The research on pore and permeability characteristics of tight sandstone reservoirs is critical for coal-measure gas development [15].

Low field nuclear magnetic resonance (LF-NMR) is a non-destructive method to characterize the pore structure parameters of complex porous media on a wide scale compared with N₂ adsorption and mercury porosimetry [1,4,17,18,19]. The sandstone sample should be saturated with water when the pore characteristics of the sandstone are obtained by LF-NMR. The water-saturated sample is then placed in a strong static magnetic field generated by an external magnet, and a small radio frequency magnetic field is superimposed on the static magnetic field to excite the hydrogen nuclei in the water, thereby inducing nuclear magnetic resonance [20]. When the radio frequency field is turned off, a signal varying with time can be received [21]. The amplitude of the signal change can be described by the longitudinal relaxation time (T₁) and the transverse relaxation time (T2). For LF-NMR, T₂ carries similar information to that of T₁ [20,22,23]. Therefore, T₂ is generally applied to the analysis of the pore structure parameters of sandstone samples. Pore sizes, porosity, pore connectivity, and pore throat distribution for tight sandstone reservoirs could be characterized by the relaxation time T₂ distribution [1,14,19,24]. However, it cannot determine the permeability of the sandstone directly [1,16]. Tight sandstone reservoirs have complex, highly heterogeneous pore structures, and poor pore connectivity [1,25]. The pore size and pore distribution vary greatly for the samples with different lithology. There is a close relationship between permeability and pore characteristics including porosity, pore-throat size, and pore volume [14,15,26,27]. The permeability of tight sandstones cannot be assessed only by total porosity because of the sandstone’s complex pore-throat geometry [26,28]. However, the movable fluid porosity attained by LF-NMR might have a certain indication on permeability [1,14].

The previous reports have studied the relationship between permeability and scaling in the water injection, pore fluid pressure, confining pressure, and effective stress [29,30,31,32]. Generally, permeability decreases with the rise of the confining pressure and the effective stress [31], the permeability declines dramatically under 4–8 MPa confining stress, and permeability reduces slightly for 8–12 MPa conditions [29,30,31]. In a deep coal-measure reservoir, stress increases with the burial depth, which results in low permeability. The extraction of coal-measure gas would increase the effective stress on pores and fractures, which results in the compression of pores and the closure of fractures [29,31,33,34,35,36,37]. The permeability of the reservoir gradually decreases with the increase of the effective stress in the process of coal-measure gas extraction [38]. This kind of phenomenon is known as the stress sensitivity of the reservoir [39]. The permeability loss by the stress sensitivity will significantly affect the water and gas production rate because the original permeability of the coal-measure reservoir is generally low [15,29,38,40,41]. The stress sensitivity coefficient of reservoir permeability (S_s) for sandstones [37,42] is an index of reservoir permeability in response to effective stress variation [38], which could be affected by the plastic mineral content, pore throat size, porosity, permeability, etc. [37]. For instance, a higher the plastic mineral content could result in a bigger S_s [37].

The effect of sandstone grains on pore characteristics, permeability, and S_s is still unclear, and the relevant research about that is of great significance to coal-measure gas production [26,37,38,43,44]. The objective of this study was to analyze the characteristics of pore systems and permeability in tight sandstones with different grains based on Coal-measure Gas Well HJD1 in Jixi Basin in Northeast China. The pore systems were studied based on LF-NMR data. The permeability was obtained by the tester based on the pulse transient method. The effects of pore characteristics on permeability variation were discussed. Then, permeability variation with effective stress and grain size of sandstones were analyzed in detail. The findings will provide a better understanding of the characterization of pore structure and permeability in the process of coal-measure gas extraction, and will be useful for the efficient development of coal-measure gas.

2. Geological Setting

Jixi Basin is mainly composed of the northern depression and the southern depression, which are separated by the central Mashan fault (Figure 1a). Large-angle normal faults are well developed in the basin. The strikes of the faults are mainly east–west and northeast.

The Quaternary in the Cenozoic and the Lower Cretaceous in the Mesozoic are the main strata in the research area where Well HJD1 is located (Figure 1). The Lower Cretaceous covers the Jixi Group and Huashan Group. The Jixi Group consists of Didao Formation, Chengzihe Formation, and Muling Formation from bottom to top (Figure 1c). The Muling Formation and Chengzihe Formation in the Lower Cretaceous are the main coal-bearing strata. Well HJD1 was constructed for coal-measure gas extraction from the Chengzihe Formation in the Jixi Basin, which is in eastern Heilongjiang province, in northeast China.

The Chengzihe Formation is the target strata in this research (Figure 1c). The buried depth of the Chengzihe Formation in Well HJD1 is 767.50–1739.05 m. The Chengzihe Formation is mainly composed of siltstone, fine sandstone, and coal seam. The sandstone samples used in this study are taken from the middle section of the Chengzihe Formation. The main coal seams involved in the sampling section are Numbers 22, 23, 25, and 28, respectively. In addition, most sandstone layers are between 2–8 m in thickness, as the sandstone layers are separated by thin mudstone layers and coal seams. The grains of sandstone also vary greatly.

3. Samples and Experimental Methods

3.1. Sample Collection and Processing

There are 4 sandstone samples collected from Well HJD1: medium sandstone (HJD1-01), fine sandstone (HJD1-06 and HJD1-08), and siltstone (HJD1-10). The 4 sandstone samples were lithologically classified according to the rock flake identification standard SY/T5368-2016 issued by the National Energy Administration in China. The grain size, and the percentage of clastic constituents and clay of the four samples can be seen in

Table 1. Rock thin section identification results of sandstone samples.

Sample No.	Clastic Constituents/%				Matrix/%	Grain Size/mm	Lithology
	Quartz	Feldspar	Detritus	Mica	Clay
HJD1-01	56	12	13	3	-	0.30–0.50	Medium sandstone
HJD1-06	32	28	13	2	23	0.05–0.10	Fine sandstone
HJD1-08	55	18	11	1	10	0.06–0.12	Fine sandstone
HJD1-10	15	11	-	-	72	0.03–0.06	Siltstone

. The appearance of the rock samples was gray white sandstone without visible cracks.

The collected sandstones were made into cylinders for permeability testing with a diameter of 50 mm and a height of 30 mm–100 mm. In addition, the flatness of the top and bottom surfaces of the sandstone samples was within 0.05 mm. Then, these samples were washed and dried before the test, in accordance with the requirements of Practices for Core Analysis (SY/T5336-2006).

HJD1-10 (silts sandstone), HJD1-06 (fine sandstone), and HJD1-01 (medium sandstone) are sandstones with different grain sizes. They were selected to undergo LF-NMR experiments. The LF-NMR experiments were conducted to characterize the pore system of the sampling sandstones and illustrate the effect of pore characteristics on the permeability of the sandstone.

3.2. Permeability Experiment

The permeability was tested by a Pulse Decay Permeameter-PDP-200 (American Core Lab Company, Tulsa, OK, USA, Figure 2), which was based on the pulse transient method. The permeability could be obtained based on the pressure decay curve. Practices for Core Analysis (SY/T5336-2006) was the reference method for this experiment, and the test gas was nitrogen. Permeability experiments were conducted by increasing the confining pressure and fixed pore pressure. This simulates the increasing effective stress during the coal-measure gas development.

In this experiment, the test sample was put into a closed container, then the initial pressure was set, and time allowed for the initial pressure to reach the equilibrium state. Then, a pulse pressure (ΔP) was applied to the top of the sample. The gas percolated through the sample under the pressure ΔP, and this process resulted in the decrease of the pressure of the top container and the increase of the pressure of the bottom container. Finally, another equilibrium state (P_f) was reached between the top container and the bottom container; there was no pressure difference attenuation.

The intake nitrogen gas pressure, which is also known as pore pressure, was set to 700 psi, and the average pore pressure stabilized between 682 psi and 704 psi. The confining pressure for each sample was set to 1100 psi, 1200 psi, 1300 psi, 1400 psi, and 1500 psi to obtain the permeability. The temperature in the permeability tests was the indoor atmospheric temperature (about 25 °C).

3.3. LF-NMR Experiments

The LF-NMR experiments were performed by the MesoMR23-060H-I instrument with a main frequency of 23.400 MHz (Figure 3). The temperature of the laboratory where the NMR experiments were performed was 23.5 °C, the magnet temperature was constant at (35 ± 0.02) °C, the echo spacing was 0.1 ms, the numbers of scans were 32, and the echo numbers were 8000.

First, the columnar sandstone samples were dried. The sample was put into a 101 electric heating blast box for nearly 24 h until its weight remained constant. In addition, the samples were vacuumed for 2 h, and then they were saturated with water for nearly 24 h in the 2XZ-4B vacuum-saturation device. The quality difference of the sandstone sample before and after saturation was less than 0.05%. Moreover, the T₂ spectrum distribution of the saturated sandstone sample was obtained by the NMR test instrument. After that, the movable water within the saturated sandstone sample was removed by the TCL-21M desktop high-speed refrigerated centrifuge. Finally, the T₂ spectrum distribution of the centrifuged sandstone samples was tested by the MesoMR23-060H-I instrument.

In an LF-NMR test, the number of hydrogen atoms present within a fluid in a porous medium can be detected by the transverse relaxation time (T₂) [1,14], and the T₂ spectrum is generally used to characterize the physical parameters of the rock, such as pore size distribution and connectivity. It is supposed that longer T₂ corresponds to larger pores, while shorter T₂ corresponds to the smaller pores [4,28]. The amplitude of the T₂ distribution reflects the number of pores within a certain size. The higher the amplitude, the greater the number of pores [20,21].

The application of NMR in the study of pore types in sandstone is based on the fact that T₂ is positively correlated with pore size. This relationship can be expressed as [20,28,45]:

$$\frac{1}{{\mathrm{T}}_2}={\mathsf{\rho }}_2\left(\frac{\mathrm{S}}{\mathrm{V}}\right)$$

(1)

where T₂ is the transverse relaxation time resulted from surface interactions, ms; and ρ₂ is a constant representing the transverse relaxation strength, μm/ms; S is the surface area of pores (cm²); and V is the pore volume (cm³).

4. Results

4.1. Permeability

The permeability of testing sandstones was between 0.351 × 10⁻³–13.910 × 10⁻³ mD under the confining pressure of 1100–1500 psi. The permeability of the medium sandstone was the highest, followed by the fine sandstone, and the siltstone was the smallest under similar pore pressure and confining pressure.

For the medium sandstone (HJD1-01), its permeability was between 11.160 × 10⁻⁴–13.910 × 10⁻³ mD under the confining pressure of 1100–1500 psi, with an average of 10.118 × 10⁻³ mD (

Table 2. Permeability results.

Sample Number	Test Gas	Confining Pressure/psi	Average Pore Pressure/psi	Permeability/×10−3 mD	Lithology	Sampling Depth/m
HJD1-01	N2	1100	695	13.910	Medium sandstone	1201.60–1201.88
	N2	1200	700	13.410
	N2	1300	699	12.860
	N2	1400	704	12.110
	N2	1500	704	11.160
HJD1-06	N2	1100	687	1.188	Fine sandstone	1300.12–1300.54
	N2	1200	695	1.081
	N2	1300	697	0.891
	N2	1400	697	0.738
	N2	1500	703	0.689
HJD1-08	N2	1100	691	1.060	Fine sandstone	1301.88–1302.5
	N2	1200	700	0.932
	N2	1300	705	0.788
	N2	1400	705	0.656
	N2	1500	704	0.594
HJD1-10	N2	1100	693	0.643	Siltstone	1380.95–1381.82
	N2	1200	707	0.571
	N2	1300	682	0.489
	N2	1400	698	0.410
	N2	1500	699	0.351

).

For the fine sandstone (HJD1-06, HJD1-08), the permeability was between 0.594 × 10⁻³–1.188 × 10⁻³ mD. The permeability of HJD1-06 was between 1.188 × 10⁻³–0.689 × 10⁻³ mD and the average permeability was 0.917 × 10⁻³ mD under 1100–1500 psi confining pressure. The permeability of HJD1-08 between 1.060 × 10⁻³–0.594 × 10⁻³ mD and the average value was 0.806 × 10⁻³ mD under the condition of 1100–1500 psi confining pressure (Table 2).

For the siltstone (HJD1-10), its permeability was between 0.351 × 10⁻³–0.643 × 10⁻³ mD, with an average of 0.493 × 10⁻³ mD (Table 2).

The grain size of sandstone has an obvious effect on permeability. The permeability of the sampling sandstone increases with the increase of grain size. The permeability of the medium sandstone (HJD1-01) with an average of 10.118 × 10⁻³ mD was higher than that of the other samples. However, the permeability of the fine sandstone (HJD1-06 and HJD1-08) and the siltstone (HJD1-10) was relatively close. The permeability of the fine sandstone was bigger than that of the siltstone under similar confining pressure and pore pressure.

The permeability and confining pressure are negatively correlated. The permeability gradually decreases as the confining pressure increases for the medium sandstone, the fine sandstone, and the siltstone (Figure 4). The decrease in permeability for HJD1-01, HJD1-06, HJD1-08, and HJD1-10 while the confining pressure increased from 1100 to 1500 psi was 2.75 × 10⁻³ mD, 0.499 × 10⁻³ mD, 0.466 × 10⁻³ mD, and 0.292 × 10⁻³ mD, respectively.

4.2. LF-NMR Pore Characteristics

The pore size distribution, total porosity, effective porosity, and the T_2C value could be obtained by the T₂ spectrum [1,14,46]. The T₂ spectra of the sampling sandstones under the water-saturated condition and the centrifugal condition is shown in Figure 5a–c. T₂ spectra for three sandstones range from 0.01 to 1889.65 ms. T₂ spectra of HJD1-01, HJD1-06, and HJD1-10 show a wide bimodal distribution with a main peak and a subpeak. There is a significant difference in T₂ distribution between the three sandstones (Figure 5d). The main peak of HJD10 is separate from the subpeak; however, the main peak of HJD1-01 and HJD1-06 is interconnected with the subpeak. The main peaks of HJD1-01, HJD1-06, and HJD1-10 are within 0.13–11.09 ms, 0.13–9.66 ms, and 0.01–1.38 ms. The subpeaks of HJD1-01, HJD1-06, and HJD1-010 are within 11.09–1889.65 ms, 9.66–666.99 ms, and 12.75–622.25 ms.

T₂ distribution is closely related to the size of the pores. Generally, the longer T₂, the bigger the pore size. In contrast, the shorter T₂, the smaller the pore size. The characteristics of the pores in sandstone could be analyzed by the distribution position and the area of the T₂ spectrum [14]. The area of the peaks reflects the number of pores within a certain size; the larger the area, the greater the number of pores. The peak width suggests the distribution of a certain kind of pore, while the number of peaks reflects the continuity of pores at all levels. The two peaks of the T₂ spectra reflect the two main types of pores. Based on the T₂ spectra curve of HJD1-01, HJD1-06, and HJD1-10, micropores correspond to T₂ < 11.09 ms, and macropores correspond to 11.09 ms < T₂ < 1889.65 ms. The micropores peak of the T₂ spectra is the largest, indicating that the micropores are the most developed. The bigger the value of T₂, the bigger the pore size of the sandstone. The pore size of the micropores from big to small is HJD1-01, HJD1-06, and HJD1-10, The pore size of the macropores from big to small is HJD1-01, HJD1-06, and HJD1-10 as well.

The T₂ spectrum morphology of the peak in the saturated state is very close to that after centrifugation (Figure 5c). This means the residual water trapped in the pores cannot be removed by centrifugation, which indicates that the connectivity of the pores is poor. Otherwise, the T₂ spectrum morphology of the peak after centrifugation is very different from the peak in the saturated state; this indicates that the connectivity of pores is good, and the pores are very conducive to gas flow. According to Figure 5a–c, the macropore connectivity in the three testing samples is relatively good, which is significantly better than that of the micropores. Furthermore, there are obvious differences in the connectivity of micropores among the three sandstone samples; the micropores’ connectivity is in the order from good to poor: HJD1-01, HJD1-06, HJD1-10.

The connection between the main peak and the subpeak could be used to identify the connectivity among pores [14]. For instance, there is a gap between the main peak and subpeak in the siltstone (HJD1-10) in Figure 5c, meaning the connection between micropores and macropores is poor. In contrast, the main peak is interconnected with the subpeak in HJD1-01 (Figure 5a) and HJD1-06 (Figure 5b), which suggests the pore connectivity of HJD1-01 and HJD1-06 is better than that of HJD1-10 between micropores and macropores. In general, the pores in the siltstone (HJD1-10) had poorer pore connectivity than that of the medium stone and the fine stone (HJD1-01, HJD1-06) [47].

The distribution position and area of the T₂ spectrum of medium sandstone, fine sandstone, and siltstone are different [47], which suggests that sandstone grains can affect pore characteristics. For example, the distribution area of T₂ spectra representing macropores in HJD1-1 (Figure 5a) is much larger than that of HJD1-6 and HJD1-10 (Figure 5b,c).

The porosity of sandstones can be analyzed based on LF-NMR T₂ [14,48]. Total porosity in the saturated state and centrifugal state can be obtained by separate NMR tests (Figure 5a–c). The maximum value of the cumulative porosity in the saturated water state is known as the total porosity [14,49]. There is residual water in the sample after centrifugation. The maximum value of the cumulative porosity after centrifugation could be seen as the residual porosity. The difference between the total porosity and the residual porosity is the porosity occupied by free water, which can be regarded as the effective porosity. The total porosity of HJD1-01, HJD1-06, and HJD1-10 was 4.14%, 2.80%, and 2.97%. The effective porosity of HJD1-01, HJD1-06, and HJD1-10 was 1.56%, 0.60%, and 0.51%. The proportion of the effective porosity to the total porosity for HJD1-01, HJD1-06, and HJD1-10 was 37.68%, 21.42%, and 17.18% (

Table 3. Results of NMR analysis.

Sample	T2C	Total Porosity	Residual Water Porosity	Effective Porosity	Pore Proportion (%)
ID	(ms)	(%)	(%)	(%)	T2 < T2C	T2 > T2C	Effective Porosity/Total Porosity
HJD1-01	5.54	4.14	2.58	1.56	61.50	38.50	37.68
HJD1-06	2.77	2.80	2.20	0.60	79.07	20.93	21.42
HJD1-10	0.85	2.97	2.46	0.51	81.95	18.05	17.17

).

The T_2C value can be obtained by the following steps. First, draw a line parallel to the X-axis with the residual porosity (Figure 5a–c). This parallel line has an intersection point with the saturated cumulative porosity curve. The X value corresponding to this intersection point is T_2C [14,50]. T_2C can divide the T₂ spectrum into two segments: one segment corresponds to pores with water that could not be drained, and the other segment corresponds to pores with water that could be drained. Pores with water that could not be drained are known as immovable pores, pores with water that could be drained are called movable pores. Therefore, the pore size at the T_2C value is taken for the separation between the immovable pore volume and the movable pore volume [14]. The T₂ spectrum which is less than T_2C corresponds to micropores with poorer pore connectivity, which are the immovable pores. The T₂ spectrum which is bigger than T_2C corresponds to macropores with better pore connectivity which are the movable pores [15]. T_2C was 5.54 ms, 2.77 ms, and 0.85 ms for HJD1-01, HJD1-06, and HJD1-10, respectively. Almost all of the micropores were immovable pores in the three samples. The proportion of immovable pores to total pores for HJD1-01, HJD1-06, and HJD1-10 was 61.50%, 79.07%, and 81.95%, respectively. The proportion of movable pores to total pores for HJD1-01, HJD1-06, and HJD1-10 was 38.50%, 20.93%, and 18.05% (Table 3).

5. Discussion

5.1. Permeability Variation with Effective Stress and Grains

The permeability decreases with the increase of the effective stress; the relationship between the permeability and the effective stress is close to the linear relation when the effective stress is between 405 psi and 808 psi because the R² of all the samples is more than 0.9757 (

Table 4. Linear fitting results between permeability (y, mD) and effective stress (x, psi).

Sample	Fitting Liner Equations	R2
HJD1-01	y = −6.95 × 10−6x + 16.86 × 10−3	0.9757
HJD1-06	y = −1.39 × 10−6x + 1.76 × 10−3	1
HJD1-08	y = −1.24 × 10−6x + 1.55 × 10−3	1
HJD1-10	y = −0.75 × 10−6x + 0.94 × 10−3	1

, Figure 6).

The grain size of sandstone has a significant impact on sandstone permeability [51]. The permeability decreases in the order of medium sandstone, fine sandstone, and siltstone under similar effective stress. For the medium sandstone (HJD1-01), the fine sandstone (HJD1-06), and the siltstone (HJD1-10), the slope in Figure 6 is −6.95 × 10⁻⁶, −1.39 × 10⁻⁶, and −0.75 × 10⁻⁶, respectively, as the effective stress increases from nearly 400 psi to 800 psi.

The rock permeability damage by the stress sensitivity could be expressed by the permeability stress sensitivity coefficient. The greater the stress sensitivity coefficient, the better the stress sensitivity will be. The calculation formula is as follows [38]:

$${\mathrm{S}}_{\mathrm{S}}=\frac{\left[1 - \sqrt[3]{\frac{{\mathrm{K}}_{\mathrm{i}}}{{\mathrm{K}}_0}}\right]}{{\log }_{10}\frac{{\mathsf{\delta }}_{\mathrm{i}}}{{\mathsf{\delta }}_0}}$$

(2)

where S_S is the permeability stress sensitivity coefficient, dimensionless; K_i is the permeability of the sample under ${\mathsf{\delta }}_{\mathrm{i}}$, mD; K₀ is the permeability under ${\mathsf{\delta }}_0$, mD; ${\mathsf{\delta }}_{\mathrm{i}} \mathrm{is}$ the effective stress at any time, psi; and ${\mathsf{\delta }}_0$ is the initial effective stress, psi.

Generally, S_s would increase for the same sample with the increase of the effective stress (

Table 5. Stress sensitivity coefficient (S_S) under different effective stress between 405 and 801 psi.

Sample Number	Lithology	Effective Stress/psi	Permeability/×10−3 mD	SS
HJD1-01	Medium sandstone	405	13.91	-
		500	13.41	0.1325
		601	12.86	0.1506
		696	12.11	0.1920
		796	11.16	0.2412
HJD1-06	Fine sandstone	413	1.188	-
		505	1.081	0.3546
		603	0.891	0.5563
		703	0.738	0.6352
		797	0.689	0.5816
HJD1-08	Fine sandstone	409	1.06	-
		500	0.932	0.4813
		595	0.788	0.5781
		695	0.656	0.6420
		796	0.594	0.6071
HJD1-10	Siltstone	407	0.643	-
		493	0.571	0.4662
		618	0.489	0.4808
		702	0.41	0.5884
		801	0.351	0.6215

). It seems that the sample with lower permeability and finer grains has a higher S_S. The permeability of the medium sandstone (HJD1-01) is much higher than that of the other samples (including HJD1-06 and HJD1-08) with similar initial effective stress, and the S_s of HJD1–01 is much lower than the other samples with similar effective stress. For the fine sandstone samples HJD1-06 and HJD1-08, the higher the permeability, the lower the stress sensitivity. This agrees with the reports that sandstones with very low permeability are affected by stress to a greater degree than those with higher permeability [52,53]. S_S could be affected by the sandstone grains. The S_s of the medium sandstone is a bit lower than that of the fine sandstone and the siltstone. However, the S_s of the fine sandstone and the siltstone is relatively close (Table 5).

5.2. Effects of NMR Pore Characteristics on Permeability Variation

Generally, the permeability of coal-measure sandstone is controlled by the number of movable pores, effective porosity, and total porosity. The total pore volume from big to small was HJD1-01, HJD1-06, and HJD1-10. The number of micropores and macropores was HJD1-01, HJD1-06, and HJD1-10 in descending order. Almost all of the micropores were the immovable pores in the three samples. The macropore connectivity affects the permeability of the tested samples. Nevertheless, the macropore connectivity in the three testing samples was relatively close. Therefore, the pore volume of the macropores or movable pores was the key factor to the permeability. Large pores are critical to the reservoir quality of the tight sandstone [50]. Movable pores, which are large scale pores with good pore connectivity, dominate the permeability of the reservoir [1,15]. The greater the number of movable pores and the larger the total porosity and the effective porosity, the bigger the permeability of the sandstone. The total porosity of HJD1-01, HJD1-06, and HJD1-10 was 4.14%, 2.80%, and 2.97%. The proportion of movable pores to total pores for HJD1-01, HJD1-06, and HJD1-10 was 38.50%, 20.93%, and 17.17%. The effective porosity of HJD1-01, HJD1-06, and HJD1-10 was 1.56%, 0.60%, and 0.51%. The permeability from big to small was HJD1-01, HJD1-06, and HJD1-10.

Grain size, compaction, and mineral composition could affect the pore structure characteristics [24,37,54]. Finer grain-size sandstones have experienced stronger compaction and cementation during diagenesis in comparison with sandstones with coarser grain size [55]. Stronger compaction and cementation tightly arranged the sandstone’s particles and decrease the residual intergranular pores. Therefore, sandstone with a finer grain size develops smaller pore space and a narrower throat [55], which contributes to less total porosity and effective porosity. Mineral composition affects pore-throat structure parameters such as porosity, pore throat, and effective porosity as well [56]. Sandstones with a coarser grain size have larger rigid grains, such as quartz and feldspar [37]. In the contrary, finer grain-size sandstones have more ductile minerals such as mica and clays [54]. Rigid grains could sustain more pressure during compaction, which is beneficial for preserving intergranular pores [57]. Meanwhile, clay minerals occupy primary pores and cut pore throats, resulting in a decrease in effective porosity. Therefore, sandstone with a coarser grain size is more likely to develop bigger total porosity and effective porosity compared with finer-grained sandstone [26]. In the testing sandstone samples, the finer the grain sizes, the less the pore space. The coarser the grain size, the larger the pore space [55]. The coarser the grains, the larger the effective porosity and the larger the permeability. This suggests that the effective porosity of sandstone has a positive correlation with the permeability value. Therefore, the effective porosity of sandstone is a sensitive indicator for evaluating the permeability of the tight sandstone reservoirs.

The effective porosity has a dominant effect on the S_s, and S_s is negatively correlated with the effective porosity. S_s of HJD1-01 was only about 0.27–0.42 times that of the other samples when the effective porosity of HJD1-01 was 2.6–3 times that of other sandstone samples. It can be seen from HJD1-10 and HJD1-06 that S_s is not only affected by the effective porosity, but also by the total porosity. The effective porosity of HJD1-06 and HJD1-10 was 0.60 and 0.51, which appears closer. S_s increases as the effective stress gradually increases. However, in a certain stress scope, the S_s of the fine sandstone (HJD-06) with higher effective porosity may be bigger than that of the siltstone (HJD-10) with lower effective porosity. It is speculated that the total porosity of sandstone also has a certain influence on S_s due to the total porosity of HJD-10 being a bit bigger than that of HJD-06.

Another reason for the increase of S_s of fine sandstone and siltstone compared to medium sandstone may be the content of plastic minerals. Clay minerals tend to increase with the decrease of sandstone grain size. The content and type of plastic minerals are one factor that determines the difference in S_s; that is, the higher the content of plastic minerals such as mica and clay, the stronger the S_s of the tight rock reservoir.

6. Conclusions

An experimental study was conducted to investigate the pore characteristics and permeability in coal-measure sandstones based on the pulse attenuation gas permeability tester and LF-NMR. The permeability variation with the effective stress and grains and the effects of NMR pore characteristics on permeability variation were analyzed in detail. The following conclusions were obtained:

(1)

Although the micropores are the most developed in sandstones from coal-measure, most of the micropores are the immovable pores. The pore characteristics are significantly affected by the grain size of sandstones in coal-measure. The movable pores and effective porosity increase with the grain size of testing sandstones. The pore connectivity ranks from good to poor with decreasing sandstone particle size.

(2)

The relationship between the permeability and the effective stress is close to the linear relationship as the effective stress is between 405 psi and 808 psi. The greater the number of movable pores and the effective porosity, the bigger the permeability of the sandstone. The effective porosity of sandstone is a sensitive indicator for evaluating the permeability of tight sandstone reservoirs. S_s would increase for the same sample with the increase of the effective stress, whilst the effective porosity is negatively correlated with S_s. The particle size of sandstone from coal-measure has a great influence on permeability and S_s. Under similar stress conditions, the permeability of the sampling sandstones increases with the increase of the grain size. The sandstone with lower permeability and finer grains has a higher S_s.