Introduction
The flowability of gas and water through coal, particularly in the micropores of coal, plays crucial roles in coalbed methane (CBM) recovery from coal reservoirs. This is even more critical for coal reservoirs with low permeability and medium-high coal ranks (
Tao et al., 2019b and
2019c). Western Guizhou and eastern Yunnan are important coal and CBM resource areas in southern China, where the Upper Permian CBM resources account for approximately 10% of the total CBM in China (
Strategy Research Center of Oil and Gas Resources Department, 2006). However, the coal reservoirs are “slightly water rich and low permeability” reservoirs (
Qin et al., 2018;
Yang et al., 2018;
Yang et al., 2019a,
2019b and
2019c;
Zhang et al., 2019;
Yang et al., 2020;
Zhang et al., 2020), leading to weak fluidity in the development of CBM in the later stage and low daily CBM production, low daily water production and a low recovery rate of CBM. Considering the physical properties of the reservoirs, it is necessary to study microscopic fluid flowability to determine the mechanism governing flowability.
Low-field nuclear magnetic resonance (NMR) analysis can quantitatively analyze pore structures and fluid-occurring characteristics by measuring the relaxation time of hydrogen-containing fluids (
1H) in the rock (
Coates et al., 2000). This method has the advantages of being noninvasive and having the ability to detect small quantities of water or oil in nanopores (<1000 nm). It has been successfully applied to physical property investigations of reservoirs and provides information on porosity, permeability, pore size distribution and movable fluid volume (
Borgia et al., 1999;
Coates et al., 2000;
Song et al., 2000;
Arnold et al., 2006;
Aguirre et al., 2007;
Talabi and Blunt, 2010;
Ahmed et al., 2014;
Mitchell et al., 2014;
Zhu et al., 2016;
Wu et al., 2019). In recent years, NMR has been increasingly used in CBM reservoir research. Researchers have carried out pore structure (
Yao et al., 2010;
Tao et al., 2018 and
2019a), reservoir descriptions (
Yao and Liu, 2012;
Zheng et al., 2018), methane adsorption (
Yao et al., 2014), wettability and pressurized water-saturated research (
Shen et al., 2018;
Sun et al., 2018), etc., based on NMR technology. However, there are few reports on the displacement of water by gas in coal samples based on NMR.
Focusing on the low-permeability reservoirs in western Guizhou and eastern Yunnan, research on the displacement of water by gas based on NMR technology has been carried out to determine the characteristics of displacing water with gas and water mobility under different pressures. The mathematical equation representing the relationship between the displacement pressure (P) and the cumulative displaced water content (Wc) was established, and the statistical equation that dictates the displacement pressure and the minimum pore diameter (d') at which the water can be displaced was established. The research results are of scientific significance for guiding CBM exploration, development and drainage control.
Samples and experimental method
Samples
In the coal-bearing synclines of Yunnan and Guizhou, China, five coal samples were collected. The coal-bearing strata in these synclines belong to the Upper Permian Longtan Formation. The coal rank is medium-high. Before sample preparation, the samples were packaged, sealed and transported to the laboratory. The prepared samples were cut into core plugs that were 2.5 cm in diameter and 5 cm in length. The displacement of water with gas by the NMR method and the porosity and permeability would be tested. The crushed samples were then measured for industrial analysis and low-temperature N2 adsorption. The vitrinite reflectance and the coal rock component were carried out (Table 1). All of the processes used abided by the national standards.
Tests on the displacement of water with gas based on NMR technology
Experiments examining the displacement of water with gas based on NMR technology under different pressure conditions were carried out in this study. The experiment instruments mainly included the following:
The NMR analyzer (MesoMR23-040H-I) was controlled at 32±0.02°C and the probe coil diameter was 25 mm. The sampling waiting time, TW, was 6000 ms and the echo time, TE, was 0.12 ms. The sampling echo number, NECH, was 18000, and the repetition number, NS, was 64. Theses parameters meet the conventional requirements.
The water-gas displacement device mainly consisted of a core holder and a humidifier. The core holder was a TY-3 core holder with a designed maximum confining pressure of 70 MPa. The maximum confining pressure was set at 12 MPa to meet the requirements. The humidifier was filled with an appropriate amount of distilled water to increase the humidity of the gas. The displacement gas was high-purity N2 stored in a high-pressure tank with a maximum pressure of over 13 MPa meeting the requirement of a maximum pressure of 10 MPa.
The type of vacuum-pressurized system is the HBJB-2, in which the RV3 type two-stage rotary vane vacuum pump was used for the vacuum process. The manual pressure pump is for pressurization. Here, a maximum pressure>40 MPa is required by the experiment (~20 MPa).
According to the following operational procedures, the sample should be dried at 100°C and then saturated with water. The drying time was ~48 h in the oven, and the weight was measured and recorded is every 8 h until it essentially did not change, at which point when the measurement was recorded as the dry weight of a sample. Then, the dry rock sample was completely immersed in distilled water for 4 h and placed in a vacuum device. The maximum pressure was 20 MPa, and the saturation is 24 h (Fig. 1(a)). Thereafter, the rock sample was removed, the water on the surface was wiped off with humid filter paper, and the core was considered saturated. At this time, it could be weighed and used to perform NMR experiments to obtain the transverse relaxation time (T2) spectrum of the saturated sample (Fig. 1(b)).
The saturated sample was placed in the core holder, and the gas line was connected. Seven points of displacement pressure (0.5 MPa, 1 MPa, 2 MPa, 4 MPa, 6 MPa, 8 MPa, 10 MPa) were designated, and a manual pressurizing device was then used to apply the confining pressure to the core holder. The confining pressure was always 2 MPa greater than the gas pressure (Fig. 1(c)). After 4 h of displacement, the sample was removed, weighed, and tested by NMR to obtain the NMR T2 spectrum under different displacement pressures (Fig. 1(b)). At the same time, the weight of residual water content (Wr) can be calculated, which is equal to the displaced coal weight minus the dried coal weight (Table 2).
Results and discussion
Pore size distribution characteristics of coal samples
The
T2 spectrum distribution curve of a typical saturated coal sample under a pressure of 20 MPa under vacuum is shown in Fig. 2. As the coal rank increases, the left peak of the
T2 spectrum drifts to the right, while the signal amplitude on the left increases, and the amplitude of the right peak signal gradually decreases. These changes are closely related to the changes in the chemical structure and pore structure of coal that occur with increasing coal rank. Generally, according to the basic principle of NMR, the
T2 of
1H in the pore water of the coal is proportional to the pore radius (
r), so the larger the pore size, the longer
T2 will be, and the smaller the pore size, the shorter the
T2 will be, as shown in Eq. (1) (
Coates et al., 2000;
Ahmed et al., 2014;
Yao et al., 2010; Kleinberg, 1996):
Equation (2) can be derived from Eq. (1):
where
ρ2 is the surface relaxation rate,
S is the pore surface area,
V is the pore volume, and
d is the pore diameter. According to this Eq. (2) and Fig. 2, medium-rank coal samples such as YCK, YL1, and YL2 have more micropores, while the high-rank coal samples DHS and LJ have larger micropores. This is obviously opposite to the general coal pore structure trend, in which the number of micropores increases as the coal rank increases (
Moore, 2012). Therefore, we need to consider the coal rank changes and make corrections. A conversion method for the
T2 spectrum and the low-temperature liquid nitrogen average pore size are adopted (
Yang et al., 2019). The BJH average pore diameter measured by low-temperature nitrogen adsorption reflects the main frequency of the pore size distribution of the micropores and transition pores to a certain extent and should roughly correspond to the peak of the left peak. Taking the average pore diameter of low-temperature nitrogen adsorption corresponding to the left peak
T2 and setting the
ρ2 of each coal rank to a fixed value, the conversion equation between
T2 and
d is established, and the
ρ2 of the coal samples of each rank is obtained (Table 3). The obtained
ρ2 is between 2.23 and 28.62 nm/ms and exhibits a decrease with an increasing coal rank. The
ρ2 calculation results of this new method are consistent with the results of the common method according to the
T2 cutoff value calculation (Zhang et al., 2018); the results have the same order of magnitude show the same characteristics of decreasing with an increasing coal rank. According to the conversion equation between the
T2 and
d of each coal sample,
T2 can be converted into d as shown in Fig. 3. It can be seen from Fig. 3 that with the increase in the coal rank, pores of
d<100 nm increase in number, and pores of
d>100 nm gradually decrease in number, where the change law is consistent with the relationship between coal pore structure and coal rank (
Levine, 1996;
Moore, 2012;
Li et al., 2017,
2019,
2020a and
2020b). At the same time, YCK and YL2 exhibit more medium-large pores (
d>100 nm) and microfractures (
d>10000 nm) than the other samples, so they show higher permeability among the five coal samples.
Characteristics of gas displacing water under different displacement pressures
By displacing the water with N2 under different displacement pressures, the T2 spectrum curves of different coal samples under different pressures were obtained (Fig. 4). The curves show that with the increase in the displacement pressure, the amplitude of the T2 spectrum signal decreases, especially for the right peak; the right half of the left peak also decreases obviously, but the amplitude of the left half of the left peak decreases less. These results show that the displacement effect is obvious in large pores and microfractures but limited in the micropores and transition pores. This means that water flowability in large pores and microfractures is better than in micropores and transition pores, and the water is referred to as producible water (Yao et al., 2010). Among the five coal samples, YCK and YL2 show the most significant decreases in the T2 spectrum amplitude. The left and right peaks of both samples decrease greatly, indicating that in these samples, the displacement effect is obvious, and water flowability is better. In contrast, the other three coal samples show no outstanding displacement effect and poorer water flowability.
The residual water content of each coal sample under different pressures is shown in Fig. 5(a). It is assumed that the vacuum samples are reach 100% water saturation when the confining pressure is increased to 20 MPa, and the residual water saturation (
Sr) at different pressures is converted (Fig. 5(b)). It can be seen from the figure that DHS and LJ exhibit the highest saturated water contents under the condition of vacuum saturation (0 MPa), whereas YL1 shows the lowest, and YCK and YL2 present intermediate values. That is to say that the high-rank coal samples exhibit a higher saturated water content, while the medium-rank coal samples exhibit a lower saturated water content. This difference occurs because high-rank coal has a complex pore structure and develops micropores (Fig. 2) (
Levine, 1996;
Moore, 2012;
Yao and Liu, 2012;
Li et al., 2017,
2019,
2020a and
2020b), and it can adsorb a large amount of liquid water. Under different displacement pressures,
Wr gradually decreases. When the displacement pressure is 0–2 MPa, the reduction of
Wr is the largest and then tends to decrease slowly. Accordingly,
Sr shows the greatest decrease at 0–2 MPa and then decreases slowly. The
Sr values of YCK and YL2 decrease the most;
Sr decreases to 30.57% and 45.48%, respectively, when the pressure is 2 MPa, indicating that the water shows strong fluidity in these samples. Accordingly, the permeability of these samples is better than that of the other samples. In comparison, the
Sr of the DHS, LJ and YL1 coal samples is still approximately 78%, indicating that water flowability in these samples is weak and that the proportion of irreducible water is high. The reason is that the high-rank DHS and LJ coals develop micropores (Fig. 3). According to the Washburn equation calculation, the micropore capillary pressure is relatively high (
Zhong et al., 2018;
Jatukaran et al., 2019). Only the displacement pressure is greater than the capillary pressure, and the remaining water can be driven out. Under the same pressure difference conditions, the irreducible water of high-rank coal is more difficult to displace than that of medium-rank coal; the ratio of irreducible water is high, and the fluidity of the water is poor. However, the weak flowability and high proportion of irreducible water in medium-rank YL1 coal is mainly due to its poor permeability, which appears to be the difference from high-rank coal.
The cumulative displacement water content (
Wc) of each coal sample (Fig. 6) increases with increasing displacement pressure. In the low-pressure stage (0–2 MPa),
Wc increases fastest. In the high-pressure stage (
P>2 MPa),
Wc tends to be stable. This relationship is consistent with the results of
Shen et al. (2018), who studied cumulative drainage water at different centrifugal pressures (0.05 MPa; 0.1 MPa; 0.5 MPa; 1 MPa; 2 MPa) in high-rank coal samples from the Qinshui Basin, China; cumulative drainage water in the low-pressure stage increases rapidly, while drainage water increases slowly when the pressure approaches 2 MPa. However, the coal sample is easily broken if the centrifugal pressure is too high, therefore the displaced water experiment cannot be carried out when the centrifugal pressure is greater than 2 MPa, and the flowability of displaced water in the high-pressure stage requires further analysis. In this study, the gas displacing water experimental method was adopted with a maximum displacement pressure of up to 10 MPa. The results indicate that the curve pattern is similar to the isothermal adsorption curve, i.e., the Langmuir curve (
Moore, 2012).
P/Wc~P is used to draw a scatter plot (Fig. 7), and the fitting degree is quite high. The highest correlation coefficient is R2 = 0.999, and R2>0.97 for most samples; only YL1 exhibits a lower value of R2 = 0.867. Therefore, the Wc and displacement pressure can be completely described by the Langmuir-like equation. The Langmuir-like equation provides a new method for calculating the cumulative displacement water content at different displacement pressures when gas displaces water.
P/Wc~P shows the following relationship:
in the Eq. (3), A is the slope, and B is the intercept. The cumulative maximum displacement water (WL) is as follows:
The key displacement pressure (PL) when Wc reaches half of WL is as follows:
The relationship between the P and the Wc can be described by a Langmuir-like equation:
Table 4 shows the Wc~P equation for all coal samples, and the fitting curves are shown in Fig. 6. The lower PL is, the steeper the Wc~P curve and the better the water flowability will be, and vice versa. For example, for YCK, the PL is smallest, and its permeability is the highest. For YL1, PL is the highest, and permeability is lowest.
The pore size allowing water displacement under different displacement pressures
According to the previous conversion equation of the T2 spectrum and the pore diameter (d), the T2 spectrum curves were converted into d distribution curves. The d distribution curves under different pressure conditions are gradually accumulated from small pores to obtain the d cumulative frequency distribution curves (Fig. 8). It is assumed that the vacuumed samples exhibited 100% water saturation when the confining pressure is increased to 20 MPa. Displacement starts at 0.5 MPa, and the water in the microfractures and large mesopores is displaced first. For pore diameter d', the final value in the pore diameter cumulative frequency distribution curve, which corresponds to the cumulative frequency curve under saturated conditions, is considered to be the minimum pore diameter at which water is displaceable under this displacement pressure, or, the pore size allowing water displacement (Fig. 8). Similarly, d' at different pressures can be calibrated (Table 5). To better understand water flowability within microscopic pores under different displacement pressures during the process of the displacement of water by gas, an analytical method was established. The results show that d' gradually decreases with the gradual increase in the displacement pressure (Fig. 9). The displacement pressure and d' conform to the power relationship (Fig. 9):
where C and D are fitting constants.
Figure 9 shows that in most of the samples, such as YCK, DHS, and LJ,
d' is close to 20 nm under a displacement pressure of 10 MPa. This is close to the calculation result of 14.41 nm for the corresponding pore diameter at a capillary pressure of 10 MPa based on the Washburn equation. For simplification, the contact angle of coal-water is 60° (
Fu et al., 1997), and the surface tension of water is 72 dyn/cm. In other words, the water in mesopores, macropores, microfractures, and some transition pores can be effectively displaced, while the water in micropores is difficult to displace. This can also explain why DHS and LJ still exhibit water saturation of 70% at the displacement pressure of 10 MPa. Although
d' is close to 20 nm at this pressure, these samples have more micropores, and the water within them is hard to displace. YL1 and YL2 have larger average pore sizes than the other samples (Table 2) and fewer micropores, but YL2 exhibits higher permeability than YL1, indicating that YL1 shows poorer pore connectivity. This is why YL1 exhibits a larger
d' than all of the other samples under different displacement pressures. Under the displacement pressure of 10 MPa, the pore size allowing water displacement is 1100 nm, which means that most of the water in the mesopores cannot be displaced. In contrast, in YL2, when the displacement pressure increases,
d' decreases continuously. At a displacement pressure of 10 MPa,
d' reaches 83 nm; i.e., the water in mesopores, macropores and microfractures can be effectively displaced.
Conclusions
This paper presents an experimental study on the displacement of water by gas in coals with low permeability and medium-high coal ranks based on nuclear magnetic resonance (NMR) technology. From this study, the following conclusions can be drawn:
1)Both Wr and Sr in coal gradually decrease as P decreases. When P is 0–2 MPa, these parameters decrease most sharply, beyond which they tend to decrease slowly. In samples with higher permeability, water shows better flowability, and Wr and Sr decrease at a higher magnitude. Moreover, high-rank coal shows weaker water fluidity and a higher irreducible proportion than medium-rank coal.
2)The relationship between P and the Wc can be described by a Langmuir-like equation, i.e., Wc = WLP/(PL + P), showing an increase in the displaced water content in coal with an increase in the displacement pressure. In the low-pressure stage (0–2 MPa), Wc increases most rapidly, while in the high-pressure stage (P>2 MPa), the displaced Wc tends to be stable.
3)d' under different displacement pressures is calibrated. The d' value decreases with an increase in the displacement pressure according to a power relationship. Furthermore, the d' values of most of the coal samples are close to 20 nm under a displacement pressure of 10 MPa. This implies that the water in micropores is difficult to displace.
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