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Article

Investigation of Stress Sensitivity of Shale Nanopores via a Nuclear Magnetic Resonance Method

by
Mingjun Chen
1,2,*,
Zhehan Lai
2,
Yili Kang
2,
Sidong Fang
1,
Hua Liu
1,
Weihong Wang
1,
Jikun Shen
2 and
Zhiqiang Chen
2
1
State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Beijing 100083, China
2
Petroleum Engineering School, Southwest Petroleum University, Chengdu 610500, China
*
Author to whom correspondence should be addressed.
Energies 2023, 16(1), 138; https://doi.org/10.3390/en16010138
Submission received: 14 November 2022 / Revised: 14 December 2022 / Accepted: 19 December 2022 / Published: 23 December 2022
(This article belongs to the Special Issue New Insights into Enhanced Oil Recovery (EOR) for Unconventional Reservoirs)
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Abstract

:
Nuclear magnetic resonance (NMR) is widely used to characterize the pore structure of rock. The nanoscale pores and fractures are well developed in a shale gas reservoir. The closure of nanopores caused by the increase in effective stress during the gas production process could induce stress sensitivity in shale nanopores, which has a great impact on the single-well productivity in the middle–late development stage. In this paper, shale samples from the Longmaxi Formation were taken to investigate the nanopore stress sensitivity via an NMR method. Samples with different degrees of pore and fracture development were selected and NMR experiments under different effective stress conditions were carried out. The results show that: (1) As the effective stress increases, the pore space in shale is continuously compressed, and the cumulative pore volume of shale decreases; (2) There is a more pronounced decrease in the cumulative pore volume of samples containing larger pores with the increase in effective stress. However, there are obvious differences in the pore volume changes in different pore sizes; (3) The transformation of nanopores of different sizes occurs in the process of effective stress loading. When the effective stress is small, the pores with diameters larger than 50 nm are mainly transformed to those with diameters of 10–50 nm. When the effective stress increases to a certain extent, the pores with diameters of 10–50 nm are mainly transformed to those with diameters of 0–10 nm; (4) There are significant differences in the compressibility of nanopores of different sizes. Larger nanopores generally have a higher compression coefficient and a stronger stress sensitivity. In the process of effective stress loading, the compression coefficient of pores with diameters between 10 and 50 nm changes relatively slowly, which can well-maintain the pore shape and quantity. Based on the variation in porosity ratio with effective stress, a new method of dividing shale nanopores is proposed; those with diameters smaller than 10 nm, those with diameters of 10–50 nm, and those with diameters larger than 50 nm.

1. Introduction

Shale gas resources are abundant and widely distributed throughout the world. It has been demonstrated to be an unconventional natural gas resource with great commercial exploitation value [1]. In contrast to a conventional natural gas reservoir, there are multi-scale pores and fractures in a shale gas reservoir from micron size to nanometer size; therefore, the gas flow behavior is characterized by the complex multi-scale gas transport mechanisms [2,3,4,5,6]. The pore pressure in a shale gas reservoir continues to decrease with the production of shale gas, inducing the increase in effective stress [7,8]. Then, the pores and fractures in shale tend to be compressed, and the gas transport capacity is significantly reduced [9,10,11]. Therefore, the shale formation damage due to stress sensitivity could be severe [12,13]. Investigating the influence of effective stress on the deformation of pores and fractures of shale could help control stress-sensitive formation damage during shale gas production and ensure the long-term stability and high production of shale gas wells.
In the past, shale stress sensitivity was generally evaluated by the changes in fracture permeability. According to research results, shale has a strong stress sensitivity, and the impact of effective stress changes on permeability is more significant than that of tight sandstone and carbonate rocks [14,15,16,17,18]. Moreover, once the stress sensitivity of shale occurs, the permeability is difficult to recover. Studies conducted on the stress sensitivity of tight sandstone and shale based on the changes in porosity and permeability with effective stress indicated that the permeability of shale is 2–3 times more sensitive to effective stress than sandstone [19]. Research performed by carrying out pressure pulse experiments on shale samples showed that shale porosity decreased linearly and permeability decreased quadratically with the increase in effective stress [20]. It was found that shale stress sensitivity is impacted by the effective stress loading method, type and arrangement of proppant, pore structure and other factors based on the results of stress sensitivity experiments in different types of shale samples [21,22].
In the middle and late stages of shale gas production, the formation pressure generally drops to the critical desorption pressure of methane. Then, a large amount of adsorbed gas in shale matrix desorbs and gradually becomes the main source of gas supply for the hydraulic fracture network [23,24,25]. The shale matrix stress sensitivity restricts the long-term high and stable production of gas wells. In the study of shale matrix stress sensitivity, it was shown that shale with a large proportion of pore size in the range of 10–50 nm has a stronger stress sensitivity based on the results of high-pressure mercury injection capillary pressure measurements [17]. Meanwhile, the organic matter in shale would lead to significant pore deformation in the matrix, and it should be pointed out that the increase in effective stress would compress the matrix pore space, thus reducing the gas transport capacity of the bulk and adsorbed phases [6,26,27].
In summary, the current research on shale stress sensitivity mainly focusses on natural fractures of micron or millimeter size and artificial fractures formed by hydraulic fracturing. However, so far, there have been few studies on shale matrix stress sensitivity, and there is a lack of corresponding experimental methods and evaluation indicators. Shale gas production is a complex process in the multi-scale flow channels. In the middle and late stages of gas production, the adsorbed gas in the matrix becomes the main source of gas supply for the hydraulic fractures. The deformation of micro- and nano-pores and fractures with the increase in effective stress would have a great impact on the gas production. Although there have been some examples in the literature investigating the pore size distribution and characterization of shale matrices [28,29,30], there is little research quantitatively evaluating the characteristics of micro- and nano-pore structure in shale matrices with the increase in effective stress. As a nondestructive method, nuclear magnetic resonance (NMR) is a relatively new core analysis method used for the characterization of pore structure of porous media and NMR can measure pores ranging from 3 nm to several microns [31,32,33]. Meanwhile, NMR has been widely used in the multi-scale pore structure characterization of shale samples [34,35]. The biggest advantage of NMR in the characterization of pore structure is that it does not cause any damage to the core [36]. Pore structure needs to be measured during effective stress loading in the stress sensitivity experiment; therefore, the combination of NMR measurements and stress sensitivity experiments can help characterize the pore structure of a core sample during effective stress loading. There are few relative studies on the stress sensitivity of shale nanopores using the method of NMR, so the study in paper is significant in better understanding the mechanisms of stress sensitivity of shale matrices. In this paper, NMR measurements of shale core samples under different effective stresses were conducted to characterize the changes in shale pore structure in microns–nanometers, which can provide experimental and theoretical support for analyzing the mechanism of gas production from shale matrices.

2. Experimental Materials and Methods

2.1. Samples Description

Shale samples from the Longmaxi Formation in China, which is a Lower Silurian marine shale gas play in the south of Sichuan Basin, were used in this work to investigate the characteristics of stress sensitivity of shale nanopores via a nuclear magnetic resonance method. The shale samples were taken from a buried depth of more than 3500 m. The results of X-ray diffraction (XRD) measurements show that the mineral composition of the samples mainly include quartz and clay minerals. The average content of quartz was 45.3% and the average content of clay mineral was 38%. Meanwhile, there was a small amount of feldspar, calcite and pyrite, the average contents of which were 7.2%, 4.3% and 5.3%, respectively. In order to investigate the response of core permeability to effective stress with different degrees of development of pores and fractures, two shale samples with similar components but large permeability differences were selected. One of them was a sample with an obvious microfracture, and the other is a matrix core sample. In the process of core selection, the microfracture sample and the matrix sample were distinguished by observation of the naked eye combined with permeability test results. The permeability and porosity of core samples were measured by the SCMS-C2 automatic porosity and permeability measurement system. The shale core samples are shown in Figure 1 and the basic parameters are shown in Table 1. It should be noted that since it is generally difficult for water to stay in the relatively large-scale fractures of cores, a core with natural microcracks was selected as the microfracture sample.

2.2. Experimental Methods

The field emission scanning electron microscopy (FESEM) measurement results show that the samples containes a large number of clay minerals, the distribution of organic matter was patchy, the micro- and nano-pores were well developed, and the size of a few organic pores was larger than 1μm. The multi-scale pore size distribution of experimental samples was characterized by the measurements of low-pressure nitrogen adsorption (LPNA), nuclear magnetic resonance (NMR) and high-pressure mercury injection capillary pressure (MICP), the results of which are shown in Figure 2.
The experimental equipment mainly included a triaxial core holder with a confining pressure pump, a core vacuum pressurized saturation device (Figure 3) and an AniMR-150 full-diameter core NMR analysis system (Figure 4). The experimental effective stress values were set according to the in situ effective stress during production of shale gas wells. It should be noted that the biggest value of effective stress during the experiments was determined by considering the abandoned gas well pressure. Meanwhile, since shale is generally rich in clay minerals, which leads to a strong creep property, the core can still reflect the pore structure under effective stress loading within a short time after unloading. In this work, the shale core samples were subjected to a series of effective stresses, which were 0, 6 MPa, 17 MPa and 35 MPa. The cyclic loading/unloading permeability tests were conducted and the results showed that although the shale permeability might recover to a very litte extent after effective stress unloading in a short time, it can still better reflect the variation characteristics of permeability with effective stress. Therefore, the loading time of each effective stress was very long (12 h) and the time interval between removing the sample from the core holder and performing the NMR experiment was very short (within 10 min). This can assure that the pore structure characterized by NMR is consistent with the pore structure in the core holder under the corresponding effective stress conditions.
The specific experimental steps are as follows:
  • The shale core samples were dried in a vacuum oven at 60 °C for 24 h, and the basic physical parameters of the cores, including length, diameter, weight and porosity, were measured;
  • The cores were put into 8% KCl solution under a liquid solution pressure of 15 MPa for 12 h and were then taken out. It should be noted that the value of 15 MPa was determined based on the in situ formation pressure of the shale gas reservoir;
  • The saturated cores were wrapped with plastic wrap and were then put into the core holder. Under constant temperature and humidity conditions, confining pressure values of 0 MPa, 6 MPa, 17 MPa and 35 MPa were applied to the core by a confining pressure pump. It should be noted that the loading time of each effective stress was 12 h and the confining pressure was equal to the effective stress in the experiment;
  • After the effective stress loading experiment, the core was removed. After gently wiping the surface water off the core sample, NMR measurements under different effective stress conditions were carried out quickly;
  • The NMR experimental results were processed to obtain the relaxation time (T2) maps under different effective stress conditions.

3. Results

3.1. NMR Relaxation Time of Shale Samples under Different Effective Stresses

In the NMR experiment, the relaxation time (T2) in porous media can be expressed as [37]:
1 T 2 = 1 T 2 B + 1 T 2 D + 1 T 2 S
where T2 is the relaxation time (ms); T2B is bulk relaxation time (ms); T2D is the diffuse relaxation time (ms); and T2S is the surface relaxation time (ms).
For cores saturated with a water solution of a certain mineralization, the diffusion relaxation time and the bulk relaxation time are extremely large compared to the surface relaxation time during the NMR experiment. The inverse of both is negligible, and the total relaxation time can be approximated as [11]:
1 T 2 ≈ 1 T 2 S = ρ 2 ( S V )
where ρ2 is the surface relaxation rate (μm/ms), the value of which is 0.01 and S/V is the surface–volume ratio (μm−1).
Through the NMR experiments, T2 maps of LMX-1 and LMX-2 under different effective stress conditions were obtained based on Equation (2). The experimental results are shown in Figure 5, and the T2 map results were statistically analyzed (Table 2, Table 3).
The experimental results show that the T2 maps of shale samples have a bimodal distribution, with the left peak distributed between 0.01–1 ms and the right peak distributed between 1–100 ms. The area of the left peak is much larger than that of the right peak. When the effective stress increased from 0 MPa to 6 MPa, the height of the right peak decreased significantly; the maximum value of the right peak of LMX-1 decreased from 76.36 to 7.88 and the maximum value of the right peak of LMX-2 decreased from 22.80 to 6.02. With the increase in effective stress, the height of the right peak continued to decrease, but relatively slowly. However, there is a certain difference in the height of the left peak. In the process of increasing the effective stress for LMX-1, the height of the left peak decreased significantly; the maximum value of the left peak decreased from 1074.46 to 805.56. When the effective stress for LMX-2 increased from 0 MPa to 17 MPa, the maximum amplitude of the left peak increased from 756.15 to 797.48, and when the effective stress increased to 36 MPa, the maximum value of the left peak decreased to 773.48. Based on the T2 shale maps, the experimental results can be further analyzed by calculating pore size, pore volume, pore cumulative volume and other parameters.

3.2. Nanoscale Shale Pore Size and Pore Volume Distribution under Different Effective Stresses

The value of T2 can reflect the internal pore volume of a shale sample. At the same time, the T2 map can reflect the pore volume distribution inside the sample. The higher peak values in T2 maps generally have a larger pore proportion at certain scale conditions. Assuming that there is a single-structure pore in a core sample, Equation (2) can be transformed into [38]:
1 T 2 = ρ 2 F S r
where r is the pore radius (μm) and FS is the pore shape factor, the values of which are 3 for a sphere, 2 for a circle, and 2 for this experiment.
Bringing the commonly used circular pore shape factor into Equation (3), then the pore radius is calculated as follows [39,40]:
r = 2 ρ 2 T 2
Based on Equation (4), the T2 maps of shale samples can be transformed into pore volume and cumulative pore volume distribution maps under various effective stress conditions. To compare the pore volume and the corresponding distribution characteristics under different effective stress conditions, the pore volume and the cumulative pore volume curves of LMX-1 and LMX-2 with different effective stresses were obtained, as shown in Figure 6 and Figure 7, respectively. Meanwhile, the nanopore size distribution of shale under different effective stress conditions is shown in Figure 8. It is worth clarifying that the pore volume distribution can characterize the amount of pore volume at different pore diameters, reflecting the size of the pore volume of different pore diameters. In contrast, the pore size distribution map characterizes how much the volume of different pore sizes accounts for the total pore volume, and reflects the size of the contribution of different pore sizes to the total pore volume. There is a difference between the two research objects, so the results also differ.
The experimental results show that the pore sizes of the samples are mainly distributed in the range smaller than 100 nm, and a small amount is distributed in the range of 100–1000 nm. With the increase in the effective stress, the pore volume of LMX-1 decreases from 2.55 cm3 to 1.91 cm3, and the total pore volume of LMX-2 decreases from 1.81 cm3 to 1.71 cm3.
In terms of pore volume, at the initial stage of effective stress loading, the pore volume of the pores with radii between 100 and 1000 nm decreases significantly, and the pore volume changes relatively slowly with the increase in effective stress. However, in the pore size range of 0–100 nm, the pore volume changes in LMX-1 and LMX-2 are significantly different with the increase in effective stress. For LMX-1, when the effective stress increased from 0 MPa to 6 MPa, the left peak representing the pore volume of pore sizes between 0 and 100 nm moved to the lower right first, and continued to move to the lower left as the effective stress continued to increase. For LMX-2, when the effective stress increased from 0 MPa to 17 MPa, the left peak representing the pore volume of pore size smaller than 100 nm moves to the upper right first, while when the effective stress increased from 17 MPa to 36 MPa, the left peak started to move to the lower left.
In terms of pore size distribution, when the effective stress increased from 0 MPa to 17 MPa, the left peaks of the pore size distribution curves of LMX-1 and LMX-2 moved to the upper right, while the pore size distribution curves moved to the lower left as the effective stress continued to increase. Compared with LMX-2, this above process of change was more pronounced in LMX-1.

3.3. Change in Nanopore Volume in Different Pore Scale

According to the nanopore classification method from the International Union of Pure and Applied Chemistry [41], the pore volumes of pores with diameter smaller than 2 nm, 2–50 nm, and larger than 50 nm under different effective stress conditions for LMX-1 and LMX-2 were calculated, respectively. The results are shown in Table 4. The variation in pore volume with effective stress in the distribution range of each pore is compared, and the experimental results are shown in Figure 9.
The results show that for LMX-1, when the effective stress increased from 0 MPa to 6 MPa, the nanopore volume of each pore distribution range decreased significantly, and the pore volume of pores with diameters larger than 50 nm decreased most obviously. In the process of increasing the effective stress from 6 MPa to 35 MPa, there are obvious differences in the variation of nanopore volume in each pore distribution range. In the pores with diameters smaller than 2 nm, the pore volume increased gradually to even higher than the pore volume under the effective stress of 0 MPa. In the pores with diameters between 2 and 50 nm, the pore volume continues to decrease, and the influence of effective stress on the pore volume at this scale gradually decreases with the increase in effective stress. When the pore diameter was larger than 50 nm, the pore volume gradually decreased with the increase in effective stress. However, for LMX-2, the nanopore volume in each pore distribution range slowly decreased with the increase in effective stress.

4. Discussion

4.1. Stress Sensitivity of Multi-Scale Nanopores in Shale

Based on the NMR experimental results of pore volume and distribution changes for the shale nanopores, the deformation mechanism of shale nanopores at different scales during effective stress loading is analyzed.
For LMX-1, at the initial stage of effective stress loading, the confining pressure of the core sample changes from the no-pressure state to the overpressure state. The nanopores of all scales are compressed and the pore volume decreases significantly. However, as the effective stress continues to increase, the pore volume of nanopores of all scales varies greatly due to the influence of rock mechanical strength, pore transformation and other factors. For pores with diameters larger than 50 nm, due to their weak mechanical strength and strong pore compressibility, the pore volume decreases significantly during the increase in effective stress. However, for pores with diameters between 2 and 50 nm, in the process of increasing the effective stress, the original pore volume at this scale gradually decreases. When the effective stress increases to a certain extent, the pore deformation at this scale is relatively stable and the pore volume does not change significantly with the effective stress. At the same time, pores with diameters larger than 50 nm continuously shift to this scale during the loading process, which further weakens the effect of effective stress on pore volume at this scale. In pores with diameters smaller than 2 nm, the pore structure is relatively stable, the mechanical properties are strong and the pore compressibility is weak. The pore structure does not change significantly with effective stress at this scale, so the effect of the effective stress on the pore volume at this scale is not obvious. However, during this process, the larger scale pore sizes decrease due to compaction, which contributes to the increase in pore volume at this scale.
However, for LMX-2, the nanopore structure of the core sample at all scales is relatively stable, the mechanical properties are strong and the pore compressibility of rock is weak. With the increase in the effective stress, the nanopores at all scales are compressed, but the change is not obvious. The initial pore shape can be well maintained, and the pore volume does not change significantly with effective stress.

4.2. A Nanopore Division Method Based on the Variation in Porosity Proportion with Various Effective Stress

In order to further investigate the stress sensitivity of multi-scale nanopores in shale, the pore distribution of samples was divided according to previous research experience, and the porosity proportion in each pore distribution range under different effective stresses was calculated. The experimental results are shown in Figure 10.
In the pores with diameter size smaller than 10 nm, the porosity ratio of the two samples decreased first and then increased with the increase in effective stress. The increase in the porosity ratio of LMX-1 occurred at the effective stress of 17 MPa, and the increase in the porosity ratio of LMX-2 occurred at the effective stress of 35 MPa. In the pore size range of 10–50 nm, with the increase in the effective stress, the porosity ratio of the two shale samples increased first and then decreased. The decrease in the porosity ratio of LMX-1 occurred at the effective stress of 17 MPa, and the decrease in the porosity ratio of LMX-2 occurred at the effective stress of 35 MPa. When the pore size is larger than 50 nm, the proportion of porosity decreases gradually with the increase in effective stress.
Based on the variation in porosity ratio with effective stress under each pore distribution, a new method for dividing nanopores is proposed. According to the variation characteristics of the porosity ratio with effective stress, nanopores in shale can be divided into those with diameters smaller than 10 nm, those with diameters of 10–50 nm, and those with diameters larger than 50 nm.
Based on the experimental results of the two samples and the multi-scale pore structure of shale, the nanopore deformation with effective stress at different scales is analyzed. In terms of pore morphology, when the effective stress increases from 0 MPa to 17 MPa, compared with other nanoscale pores, pores with diameters between 10 and 50 nm can better maintain the pore morphology. With the continuous increase in the effective stress, the deformation of nanopores tends to be stable. In terms of the pore-scale displacement, when the effective stress increases from 0 MPa to 17 MPa, the pore displacement is mainly from pores larger than 50 nm to pores between 10 and 50 nm. When the effective stress increases from 17 MPa to 35 MPa, the pore displacement is mainly from pores larger than 10–50 nm to pores between 0 and 10 nm.

4.3. Variation Characteristics of the Compression Coefficient for Multi-Scale Nanopores under Different Effective Stresses

In porous media such as shale, the compressibility of pores can be generally quantitatively characterized by the compression coefficient:
C i = 1 ϕ i ∂ ϕ i ∂ P c
where Ci is the pore compressibility (MPa−1); ϕi is the pore porosity (%); and Pc is the effective pressure (MPa).
Based on the NMR T2 map for shale samples saturated by an aqueous phase, Equation (5) can be written as follows:
C i = 1 ϕ i ∂ ϕ i ∂ P = 1 V iPc V iP c − V iP 0 P c − P 0 = 1 − A iP c P c − P 0
where AiPc = ViPc/ViPo; ViPc and ViPo are the corresponding volume of pores at the effective stresses Pc and P0 (cm−3), respectively.
Based on the method of dividing nanopores with the variation in porosity ratio with effective stress, the compression coefficients of nanopores of different scales under different effective stress conditions were calculated, and the results are shown in Figure 11.
The experimental results show that for LMX-1, the compression coefficients of the nanopores decrease with the increase in effective stress. The compression coefficient for pores with diameters smaller than 10 nm decreases from 0.0445 MPa−1 to 0.0002 MPa−1, which is a reduction of 99.55%. The compression coefficient for pores with diameters larger than 50 nm decreases from 0.0998 MPa−1 to 0.0230 MPa−1, which is a reduction of 76.93%. The compression coefficient of pores with diameters between 10 and 50 nm decreases from 0.0131 MPa−1 to 0.0068 MPa−1, which is a reduction of 34.45%, indicating that the compression coefficient decreases relatively slowly. For LMX-2, the compression coefficients of nanopores at different scales vary with the increase in effective stress. The compression coefficient of pores with diameters smaller than 10 nm decreases from 0.0206 MPa−1 to 0.0041 MPa−1, which is a reduction of 77.49%. The compression coefficient of pores with diameters larger than 50 nm decreases from 0.0575 MPa−1 to 0.0129 MPa−1, which is a reduction of 76.93%. The compression coefficient for pores with diameters between 10 and 50 nm increases from −0.0196 MPa−1 to −0.0046 MPa−1. The compression coefficient is negative and increases with the increase in effective stress.
In general, shale nanopores with larger sizes have a larger compression coefficient, and the pores are more easily compressed. Therefore, the stress sensitivity of shale with larger nanopores is higher. Additionally, the corresponding compression coefficient decreases more significantly with the increase in effective stress. However, in the LMX-2 shale sample, the compression coefficient of pores with diameters between 10 and 50 nm is negative, which is mainly caused by the increase in the number of nanopores at this scale. Compared with pores of other scales, pores with diameters ranging from 10–50 nm can maintain pore morphology better during effective stress loading.

5. Conclusions

(1)
With the increase in the effective stress, the cumulative pore volume of shale decreases by 5.52–25.10%, and the pore space is continuously compressed. In terms of pore volume, during the effective stress loading process, the pore volume of shale decreases significantly in pores with diameters between 100 and 1000 nm. In the pores with diameters smaller than 100 nm, the pore volume of shale samples with natural fractures decreases with the increase in effective stress, while the pore volume of shale matrix samples increases.
(2)
When the effective stress is small, the pores with diameters between 10 and 50 nm can maintain the pore morphology better than those at other scales. With the continuous increase in the effective stress, the deformation of nanoscale pores tends to be stable. In terms of the pore-scale transformation, when the effective stress is small, the pores with diameters larger than 50 nm are mainly transformed to 10–50 nm diameter pores. When the effective stress increases to a certain extent, the pores with diameters between 10 and 50 nm are mainly transformed to those with diameters smaller than 10 nm.
(3)
The compression coefficients of nanopores of different scales under different effective stresses were calculated by NMR T2 maps. Shale with larger nanopores has a larger compression coefficient and a stronger stress sensitivity. With the increase in effective stress, the stress sensitivity of shale gradually lowers. Compared with other sized pores, the change in the compression coefficient of pores with diameters between 10 and 50 nm is relatively slow during effective stress loading, which can help maintain pore morphology.
(4)
Based on the variation characteristics of the porosity ratio with effective stresses for each pore distribution, a new method for dividing nanopores is proposed. According to the variation in porosity ratio with effective stress, the nanopores in shale can be divided into those with diameters smaller than 10 nm, those with diameters of 10–50 nm, and those with diameters larger than 50 nm.

Author Contributions

Conceptualization, M.C. and Y.K.; Methodology, M.C., Z.L. and W.W.; Software, S.F., J.S. and Z.C.; Investigation, M.C., Z.L., Y.K., J.S. and Z.C.; Resources, H.L.; Writing—original draft, Z.L.; Writing—review & editing, M.C., S.F., H.L. and W.W.; Supervision, Y.K. and H.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Open Fund of State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development under a grant number 33550000-21-ZC0613-0335 and National Natural Science Foundation of China under a grant number 41902154.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data available on request from the authors.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Morphology of experimental shale samples. (a) LMX-1 (a sample with microfracture) (b) LMX-2 (a matrix sample).
Figure 1. Morphology of experimental shale samples. (a) LMX-1 (a sample with microfracture) (b) LMX-2 (a matrix sample).
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Figure 2. Multi-scale pore size distribution. (a) LMX-1 (b) LMX-2.
Figure 2. Multi-scale pore size distribution. (a) LMX-1 (b) LMX-2.
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Figure 3. Core vacuum pressurized saturation device.
Figure 3. Core vacuum pressurized saturation device.
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Figure 4. AniMR-150 full-diameter core NMR analysis system.
Figure 4. AniMR-150 full-diameter core NMR analysis system.
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Figure 5. T2 maps of shale samples under different effective stress conditions. (a) LMX-1 (b) LMX-2.
Figure 5. T2 maps of shale samples under different effective stress conditions. (a) LMX-1 (b) LMX-2.
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Figure 6. Pore volume distribution under different effective stress conditions. (a) LMX-1 (b) LMX-2.
Figure 6. Pore volume distribution under different effective stress conditions. (a) LMX-1 (b) LMX-2.
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Figure 7. Cumulative pore volume distribution under different effective stress conditions. (a) LMX-1 (b) LMX-2.
Figure 7. Cumulative pore volume distribution under different effective stress conditions. (a) LMX-1 (b) LMX-2.
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Figure 8. Nanopore size distribution of shale under different effective stress conditions. (a) LMX-1 (b) LMX-2.
Figure 8. Nanopore size distribution of shale under different effective stress conditions. (a) LMX-1 (b) LMX-2.
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Figure 9. Variation in nano pore volume with effective stress at different scales. (a) LMX-5 (b) LMX-6.
Figure 9. Variation in nano pore volume with effective stress at different scales. (a) LMX-5 (b) LMX-6.
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Figure 10. Variation in porosity ratio with effective stress under each pore distribution. (a) LMX-1 (b) LMX-2.
Figure 10. Variation in porosity ratio with effective stress under each pore distribution. (a) LMX-1 (b) LMX-2.
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Figure 11. The variation of compressive coefficient of nanoscale pores with effective stress. (a) LMX-1 (b) LMX-2.
Figure 11. The variation of compressive coefficient of nanoscale pores with effective stress. (a) LMX-1 (b) LMX-2.
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Table
Table 1. Basic parameters of shale samples.
Table 1. Basic parameters of shale samples.
NumberLength/mmDiameter/mmTOC/wt%Clay Mineral Content/%Porosity/%Permeability/mD
LMX-138.4625.242.7936.14.530.300
LMX-238.1225.202.6638.03.940.080
Table
Table 2. Statistical results of T2 maps for LMX-1.
Table 2. Statistical results of T2 maps for LMX-1.
Effective Stress
/MPa		Left PeakRight Peak
Start Time/msPeak Time
/ms		End Time
/ms		Peak Ratio
/%		Start Time/msPeak Time
/ms		End Time
/ms		Peak Ratio
/%
00.010.764.6496.8810.7228.4857.223.12
60.011.003.5199.8032.7575.65132.190.20
170.010.873.5199.7928.4865.79132.190.20
350.010.673.0599.519.3224.7757.220.49
Table
Table 3. Statistical results of T2 maps for LMX-2.
Table 3. Statistical results of T2 maps for LMX-2.
Effective Stress
/MPa		Left PeakRight Peak
Start Time/msPeak Time
/ms		End Time
/ms		Peak Ratio
/%		Start Time/msPeak Time
/ms		End Time
/ms		Peak Ratio
/%
00.010.573.0598.736.1418.7837.651.27
60.010.663.0599.4112.3328.4857.220.59
170.010.753.0599.5718.7443.2875.650.43
350.010.752.6699.5218.7443.2886.970.48
Table
Table 4. Nanopore volumes under different effective stresses.
Table 4. Nanopore volumes under different effective stresses.
Pore DiameterLMX-1 Pore Volume (cm3)LMX-2 Pore Volume (cm3)
0 MPa6 MPa17 MPa36 MPa0 MPa6 MPa17 MPa36 MPa
0~2 nm0.12530.08310.10260.13110.16480.12750.11840.1169
2~50 nm2.21211.87841.80901.80421.60081.59941.58111.5757
>50 nm0.21180.08500.06690.03570.03870.02530.02270.0207
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Chen, M.; Lai, Z.; Kang, Y.; Fang, S.; Liu, H.; Wang, W.; Shen, J.; Chen, Z. Investigation of Stress Sensitivity of Shale Nanopores via a Nuclear Magnetic Resonance Method. Energies 2023, 16, 138. https://doi.org/10.3390/en16010138

AMA Style

Chen M, Lai Z, Kang Y, Fang S, Liu H, Wang W, Shen J, Chen Z. Investigation of Stress Sensitivity of Shale Nanopores via a Nuclear Magnetic Resonance Method. Energies. 2023; 16(1):138. https://doi.org/10.3390/en16010138

Chicago/Turabian Style

Chen, Mingjun, Zhehan Lai, Yili Kang, Sidong Fang, Hua Liu, Weihong Wang, Jikun Shen, and Zhiqiang Chen. 2023. "Investigation of Stress Sensitivity of Shale Nanopores via a Nuclear Magnetic Resonance Method" Energies 16, no. 1: 138. https://doi.org/10.3390/en16010138

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