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. 2024 Sep 6;9(37):38599–38617. doi: 10.1021/acsomega.4c04176

Study on the Dispersion Characteristics of Coal Complex Resistivity under the Effect of Liquid Nitrogen Cyclic Freeze–Thaw and Evaluation of Permeability Enhancement

Jian Li †, Xiaokai Xu ‡,*, Yugui Zhang †, Hang Zhang §, Haihai Hou ∥, Lin Tian ⊥, Kuo Jian #, Zhengzheng Xue ‡, Zehua Zhang ‡
PMCID: PMC11411684  PMID: 39310203

Abstract

graphic file with name ao4c04176_0024.jpg

The effect of liquid nitrogen freeze–thaw fracturing on coal seams can be potentially evaluated by the complex resistivity method. The real part (Reρ) and the imaginary part (Imρ) of the complex resistivity and permeability of coal were determined under different cycle times and in different bedding directions. The reason for permeability enhancement was discussed, and the dispersion mechanism of complex resistivity during cyclic freeze–thaw fracturing was analyzed. The results indicated that (1) the complex resistivity parameters have a good response to the cycle times; Reρ, |Imρ|, and the dispersion degree (α) are positively correlated with cycle time; the fully polarized frequency (fp) of Reρ, the characteristic frequency (fc) of Imρ, and variation are negatively correlated with cycle time. (2) The difference in complex resistivity parameters between the vertical bedding direction and the parallel bedding direction is significant, and the difference in electrical properties of the bedding structure continuously decreases with the increase in cycle time. (3) Under the effect of liquid nitrogen cyclic freeze–thaw, a complex network of fractures in coal is formed, the anisotropic characteristics of coal are weakened, and effective conductive channels are damaged. The peak frost heave force decreases exponentially with the increase in cycle time, and the difference in bedding electrical properties gradually disappears. (4) Comparing the inversion degree of measured data with three conductive models, ρ0 and τ are selected as the optimum parameters for evaluating the effect of liquid nitrogen cyclic freeze–thaw. A logarithmic permeability evaluation model is constructed based on ρ0 and τ. This work provides a new perspective based on electrical detection for evaluating the permeability enhancement of coal during liquid nitrogen cyclic freeze–thaw.

1. Introduction

With the development of society and the improvement of economic levels, the global energy demand is also growing.1 However, the supply–demand contradiction of conventional oil and gas reservoir resources is gradually increasing,2 and the effective development of unconventional oil and gas reservoirs is particularly vital.3,4 Among them, coalbed methane (CBM), as an early developed energy, has made positive contributions to ensuring national energy and resource security.5−7 The heterogeneity of gas content in coal is high, while permeability (less than 1 mD), reservoir pressure, and gas saturation are low.8 These factors affect the efficient development of CBM. Reconstructing the pores and fracture structure of coal is the key to accelerating the current progress of the industry.9−11 Liquid nitrogen cyclic freeze–thaw fracturing has the advantages of a high frost heave force (about 207 MPa), an ultralow temperature (−196 °C), a high compression ratio (1:696), and no water locking effect. It also effectively avoids problems, such as groundwater pollution and damage to coal reservoirs. Hence, it is widely used in the field of CBM extraction.12−14

Previous studies have shown that the effectiveness of liquid nitrogen freeze–thaw fracturing technology depends on factors such as the metamorphism degree of coal and rock,15 water saturation,16 temperature differences,17 and freeze–thaw frequency.18 Its fracturing principle is mainly the combined effect of temperature force generated by low-temperature action, frost heave force from water and ice phase change, and expansion force from liquid nitrogen gasification.19 The accurate evaluation of the liquid nitrogen freeze–thaw fracturing effect of coal and rocks plays an important role in the development of the CBM industry. At present, relevant scholars have used various monitoring methods to study the liquid nitrogen freeze–thaw fracturing effect of coal and rocks. Li et al. found that the heat transfer law of coal samples exhibited the notable three-stage distribution during the process of liquid nitrogen fracturing20 and pointed out that the freeze–thaw cycle could reduce the uniaxial stress yield limit of coal.21 Du et al.22 believed that due to the high elastic modulus of sandstone, its tensile strength and maximum tensile stress generated by contact with liquid nitrogen were superior to coal, resulting in a larger damage area in the coal than sandstone. Zhang et al.23 proposed that the permeability of coal gradually increased with the increase of its water content and the cycle times. Zhang24 believed that the acoustic emission events of coal samples with the same temperature but different freeze–thaw cycle times mainly occur in the yield stage and failure stage. Li et al.25 used SEM to observe the changes in the surface morphology of coal samples induced by the liquid nitrogen and found that as the cycle times increased, the width of coal surface fractures evolved from microscopic to macroscopic. Akhondzadeh et al.26 accurately compared the changes in the internal pore and fracture structure of coal before and after liquid nitrogen fracturing through 3D X-ray microcomputed tomography and proposed that the porosity of coal increased by more than 11% after liquid nitrogen fracturing. Chu et al.27 used nuclear magnetic resonance (NMR) technology to study the pore and fracture structure of liquid nitrogen freeze–thaw coal and believed that liquid nitrogen freeze–thaw technology promoted the development of coal pores, increasing the total porosity, residual porosity, and effective porosity of coal. However, there were certain limitations in the evaluation methods. The measurement and monitoring of the temperature field, pressure field, and permeability of coal were traditional evaluation indicators that required an in-depth study from the perspective of other physical properties of coal; acoustic emission technology was prone to measurement errors caused by noise interference; the testing accuracy of CT scanning and NMR technology was high, but the measurement cost was also high. There is an urgent need for a fast, effective, and cost-effective evaluation method to characterize the freeze–thaw effect of liquid nitrogen.

The complex resistivity method uses alternating currents of different frequencies to measure the electrical parameters of the medium and obtains the parameter distribution pattern of the medium in the continuous time or frequency domain, which is its spectral characteristics.28 This method is widely used in soil monitoring of heavy metals and organic pollutants,29,30 medical pathology monitoring,31,32 and other fields. It is also helpful for basic experiments and on-site investigations in the field of nonferrous metal mineral exploration,33 oil and water layer identification,34 shale gas development,35 and hydraulic fracturing effect evaluation.36 The main cause of the dispersion of dielectric complex resistivity is the polarization between the electrons or ion conductors inside the sample and the charged particles in the solution at the interface of pores and fractures.37 The complex electrical dispersion of coal and rock is mainly determined by factors such as water saturation,38 lithological characteristics,39 temperature,40 and stress conditions41 during measurement. In addition, the shape, structure, and connectivity of pores and fractures have a crucial impact on the complex resistivity.42 Kruschwitz and Yaramanci43 found that the changes in complex resistivity and phase composition of rocks are caused by the spatial distribution of pores and the storage state of pore water. Li et al.44 studied the effect of different fracture widths on the relationship between resistivity at different frequencies and water saturation. Liu et al.45 studied the effects of fracture width, density, and dip angle on resistivity through rock physics experiments and derived a normalized rock resistivity formula. Scholars have proposed various models for studying the electrical properties of rock and coal, including the Cole–Cole model,46 Dias model,47 Debye model,48 etc. Therefore, considering the significant effect of the complex resistivity method on characterizing the structure of coal pores and fractures, the application of this method to evaluate the freeze–thaw effect of coal liquid nitrogen has a certain research value.

In addition, coal is a natural heterogeneous porous material composed of a coal matrix, primary fractures, and mineral impurities. The formation of coal and its evolution with geological bodies determine the spatial distribution characteristics of mineral inclusions and primary fractures within the coal, resulting in complex heterogeneous microstructures and bedding distribution characteristics within coal. This causes the coal to exhibit anisotropic characteristics in permeability,49 acoustic waves,50 and mechanical properties.51 Regarding the anisotropy of its electrical properties, Shen et al.52 studied the relationship between electrical anisotropy and fracture parameters. Meng et al.53 discovered that the complex electrical characteristics of coal in the direction of the face cleat, butt cleat, and vertical bedding were anisotropic. Chai et al.54 pointed out that there were significant anisotropic characteristics of resistivity in the strike, dip, and vertical directions of coal. However, further research is needed on the anisotropy characteristics of coal complex resistivity under liquid nitrogen cyclic freeze–thaw conditions.

In summary, liquid nitrogen cyclic freeze–thaw fracturing technology can significantly improve the fracture structure of coal.55 The complex resistivity dispersion of coal is sensitive to the degree of fracture development and the bedding structure.56,57 Therefore, based on a self-made experimental platform, complex resistivity and permeability tests were conducted using low-permeability coal seams as the research object. The impact of liquid nitrogen freeze–thaw fracturing technology on the complex electrical performance of coal was analyzed, the decisive and restrictive effects of cycle times and the bedding structure on the liquid nitrogen fracturing degree of coal were assessed, and the liquid nitrogen fracturing evaluation model was established based on the advantageous parameters of coal complex electricity. This research fills the gap of relatively few electrical evaluation methods for the freeze–thaw effect of coal liquid nitrogen. The complex resistivity method used considers the induced polarization effect caused by the polarization properties of coal, which can obtain characteristic frequency parameters under a continuous loading frequency. Moreover, this method only needs a shorter testing time and lower testing cost, and it provides a new idea for evaluating the liquid nitrogen fracturing effect using the frequency dispersion characteristics of coal complex resistivity and offers a basis for improving the permeability of CBM.

2. Samples and Experiments

2.1. Sample Collection and Preparation

The test sample for this experiment is obtained from the 3# coal seam of the Permian Shanxi Formation in the Sihe Coal Mine, Shanxi Province. The sample collection area is located in the Qinshui Basin. The characteristics of the fold structure in the Qinshui Basin are influenced by regional distribution, with the southern and northern parts mainly trending in a nearly north–south direction and local parts trending in a nearly east–west and northeast direction. The folds in the central part are mainly developed in a north–northeast and northeast direction; the western part is characterized by the superposition of Mesozoic folds and Cenozoic normal faults. The geological structure conditions of the Sihe Coal Mine are simple, the coal seam dip angle is gentle, the small structures of the mine are not well developed, and the occurrence pattern of CBM is strong. The existing geological conditions of the coal mine are among the most superior in China, and it is an extremely important high-rank CBM industrial park in China, as shown in Figure 1.58−60 By observation of the development of coal fracture bedding, coal samples with fewer primary fractures are selected. After being cut by the cutting machine, drilled by the coring machine, and polished by the polishing machine, large coal blocks are drilled according to the vertical and parallel bedding directions of coal. The coal pillar dimensions are Φ50 mm × L100 mm, and the following samples are referred to as Va, Vb, Pa, and Pb, respectively. The basic physical parameters of the test samples using the pile coning and quartering method are shown in Table 1.

Figure 1.

Figure 1

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Geological overview of the research area (adapted from refs (58–60)).

Table 1. Analysis and Test Results of Coal Sample Physical Parametersa.

metamorphic degree maximum reflectivity of vitrinite oil immersion/% industrial analysis/%
 elemental analysis/%
  Ro,max Mad Aad Vdaf Fcad Cdaf Hdaf Ndaf Sdaf Odaf
anthracite 2.76 1.68 9.24 6.71 82.37 89.79 2.61 1.68 0.36 5.56
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a

Notes: Ro,max is the maximum reflectivity of vitrinite oil immersion, %; Mad is the percentage of moisture, %; Aad is the percentage of air-dried ash, %; Vdaf is the percentage of volatile matter on a dry ash-free basis, %; Fcad is fixed carbon, %; Cdaf is the anhydrous and ash-free organic carbon content, %; Hdaf is the anhydrous and ash-free organic hydrogen content, %; Ndaf is the anhydrous and ash-free organic nitrogen content, %; Sdaf is the anhydrous and ash-free organic sulfur content, %; Odaf is the anhydrous and ash-free organic oxygen content, %.

2.2. Experimental Program

The measured sample was placed into a dewar bottle filled with −196 °C liquid nitrogen, and the continuous immersion time of a single freezing step was 15 min. Then, the samples were kept in a pretemperature device at a temperature of 50 °C for 20 min, which is considered a complete freeze–thaw cycle process. During the process, samples were completely immersed in liquid nitrogen, and liquid nitrogen was added in time to ensure the integrity of the liquid nitrogen freeze–thaw effect. The overall experimental process is shown in Figure 2. The experimental methods and steps are as follows:

  • (1)

    According to the results of industrial analysis, the average natural moisture content of the measured sample was 1.68%. The maximum moisture contents of the four samples (Va, Vb, Pa, and Pb) were calibrated with a constant-temperature drying oven and a vacuum-saturated water instrument using the weighing method, and the values were 4.06, 4.53, 5.24, and 6.72%, respectively. To ensure consistency in moisture conditions, the moisture content of the freeze–thaw sample was unified to 2%.

  • (2)

    The LCR device, calibrated by operations such as open-circuit compensation, short-circuit compensation, and line compensation, was connected to the measured sample with copper conductive paper pasted on both ends through a Kelvin fixture. The constant current of the device was set to 0.001 mA, the testing frequency range was 1 Hz to 200 kHz, and the number of measurement frequency points was 60. The dispersion response characteristic of sample complex resistivity before liquid nitrogen cyclic freeze–thaw fracturing was monitored.

  • (3)

    The permeability of samples before liquid nitrogen cyclic freeze–thaw fracturing was measured using a seepage device. To simulate the actual in situ stress and pore pressure state of the coal reservoir, according to the relevant ref (61), CH4 was selected as the seepage gas, and the axial pressure of samples was varied in gradients of 1, 1.5, 2, 2.5, and 3 MPa. The confining pressure remained stable at 5 MPa. In order to avoid the passage of gas through the gap between the sample and its external rubber sleeve, the pore pressure should be at least 2 MPa less than the confining pressure. Thus, the pore pressure was set to 1 MPa.

  • (4)

    Liquid nitrogen was injected into the dewar bottle until its state stabilized. Then, the measured sample was immediately placed into the bottle. According to the relevant ref (62), liquid nitrogen freeze–thaw treatment was performed according to the designed cycle times (4, 8, 12, 16, and 20). Steps (1), (2), and (3) were repeated to obtain the dispersion response characteristics and permeability of the measured sample after different freeze–thaw treatments.

Figure 2.

Figure 2

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Experimental process diagram.

In addition, in the initial state and final state of the liquid nitrogen freeze–thaw cycle treatment, CT scanning was performed on the measured sample to obtain the visual changes in the fracture distribution of coal.

Notes: the experimental samples for complex resistivity, permeability, and CT scan measurements were coal pillars that were naturally left to stand for 48 h.

3. Results and Discussion

3.1. Conductive and Dielectric Mechanism of Coal

There are two forms of charge carriers in coal: ions and electrons. Ionic conductivity refers to the phenomenon where ions in coal pores and fracture channels migrate in a certain direction under the effect of an external electric field, generating an electric current. The magnitude of the ion migration rate determines the conductivity of coal. Factors affecting the ion migration rate include ion properties, solution concentration, temperature, and electric field strength. Electronic conductivity refers to the ordered and directional movement of free electrons in coal under the effect of an electric field. The properties of free electrons and the number of electrons that overcome potential barriers and transition to the conduction band determine the magnitude of the electronic conductivity. The conductivity of coal is determined by several conditions such as the fracture structure, water content, free radicals, and macromolecular structure.

In addition, the dielectric properties of coal are mainly divided into two parts: the micropolarization mechanism and macro-induced polarization mechanism. At the microscopic level, the positive and negative charge centers of polar molecules (H2O molecules) do not coincide, and there exists an inherent dipole moment. However, due to the irregular motion of molecules in the absence of an electric field, the macroscopic dipole moment of the dielectric molecule as a whole is equal to zero. After applying the electric field, relative elastic displacement occurs between the positive and negative charge centers of the molecule. Moreover, the molecule also gradually turns toward the direction of the electric field due to the effect of the electric field torque. In summary, the electric moment along the field strength direction inside the dielectric is not zero. That is, under the effect of the electric field, the coal displays a macroscopic dipole moment along the field strength direction inside. Dielectric polarization can be mainly divided into electron displacement polarization, ion displacement polarization, orientation polarization, and interface polarization.63 As shown in Table 2, different polarization forms correspond to different polarization frequency bands; that is, the completion time of polarization is different. The order of arrangement is tinterface polarization > torientation polarization > tion displacement polarization > telectron displacement polarization.64

Table 2. Microscopic Polarization Form of Coal64.

3.1.

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Induced polarization of coal is the main research object for studying its electrical dispersion properties. Due to the excitation of the electric field, both positive and negative charges inside the coal undergo differentiation and migration. On the basis of the primary voltage V1, the “overpotential” V2 is generated, and the two are combined to form the total field potential difference V, which includes the potential difference of the power supply electric field and the polarization potential difference. Both V2 and V vary with time, and the variation pattern is shown in Figure 3a. According to the internal composition and geological environment of the coal, its induced polarization can be achieved by the combined action of electron conductor-induced polarization (Figure 3b) and ion conductor-induced polarization. Ionic conductor-induced polarization can be subdivided into double-layer deformation (Figure 3c) and thin-film polarization (Figure 3d).65,66

Figure 3.

Figure 3

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Macropolarization form of coal (adapted from refs (65 and 66)).

3.2. Influence of Liquid Nitrogen Cyclic Freeze–Thaw on the Dispersion Characteristics of Coal Complex Resistivity

3.2.1. Effect of Different Cycle Times on the Dispersion Characteristics of Coal Complex Resistivity

To analyze the effect of cycle times on the dispersion of coal complex resistivity, an LCR device was used to measure the complex electrical parameters Reρ and Imρ of coal under the initial state, 4th, 8th, 12th, 16th, and 20th cycle conditions, as shown in Figures 4–7.

Figure 4.

Figure 4

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Dispersion curve of complex resistivity with different cycle times for sample Va.

Figure 7.

Figure 7

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Dispersion curve of complex resistivity with different cycle times for sample Pb.

Figure 5.

Figure 5

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Dispersion curve of complex resistivity with different cycle times for sample Vb.

Figure 6.

Figure 6

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Dispersion curve of complex resistivity with different cycle times for sample Pa.

As shown in the above figure, regardless of the bedding direction of the coal sample, the variation trend of the dispersion curves of Reρ and Imρ is consistent. Specifically, with the increase in frequency, the Reρ value continuously decreases, the decreasing rate gradually accelerates, and then the decreasing rate gradually slows down, forming a slide shape. The Imρ value is negative, which first decreases with a continuously increasing decrease rate and then converts to a numerical increase, and the increasing rate gradually decreases, forming a valley shape. The mutation frequency during the acceleration of the Reρ decreasing rate is defined as the fully polarized frequency (fp). The conversion frequency of the Reρ and Imρ dispersion curves is almost consistent. Therefore, this frequency is defined as the characteristic frequency (fc). From a visual perspective, the variation in the dispersion curve of Imρ is more significant than that of Reρ.

The reason for this variation trend is as follows. As an organic sedimentary rock, coal contains many inorganic mineral components, such as clay components (kaolinite), carbonate minerals, etc., as shown in Figure 8. The mineral components in the test samples of the study area are mainly kaolinite, dolomite, and cristobalite, with contents of 84.3, 12.7, and 3%, respectively. The data show that the dielectric constant of kaolinite is 28.29–49.14, indicating good conductivity.67 In addition, coal also has basic structural units mainly composed of aromatic nuclei connected by bridge bonds, which may have a significant impact on its conductive and dielectric properties. The metamorphism degree of coal in the study area is high-rank anthracite with a high carbon content. The structure of coal is mostly ordered, and there are π bonds formed by π electrons, which tend to form a graphitic structure with a strong electron conductivity. The ion conductivity of water containing coal is also an important component of the coal’s electrical properties. Based on the polarization mechanism of coal mentioned above, for Reρ, the dispersion curve is caused by the polarization type and degree of polarization completion of its own charged particles with frequency changes. The higher the frequency, the shorter the supply time for charged particle polarization, the greater the difficulty of polarization completion, and the fewer the types of polarization. Therefore, the lower the potential difference, the smaller the test resistance value. Among them, fp represents the frequency value at which the coal almost completes the polarization. For Imρ, the dispersion curve shows capacitance characteristics and depends on the combined coupling effect of the capacitance value of the coal itself and the loading frequency. As shown in Figure 9 and eqs 1 and 2, the measured Imρ value is highly consistent with the calculated Imρ value.68

3.2.1. 1
3.2.1. 2
Figure 8.

Figure 8

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Mineral composition analysis of coal samples.

Figure 9.

Figure 9

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Relationship curve between the real and imaginary parts of complex resistivity and capacitance.

Notes: Imρ is the imaginary part of the complex resistivity of coal, kΩ·m; Xc is the imaginary part of the complex resistance of coal, kΩ; A is the measured electrode area, m2; l is the coal pillar height, m; f is the frequency, Hz; C is the capacitance of coal, μF.

As shown in Tables 3 and 4 and Figures 4–7, the parameter Reρf=1 with the highest polarization degree at 1 Hz in the coal Reρ dispersion curve and the parameter Imρmin at the characteristic frequency point in the Imρ dispersion curve are taken as examples. As the cycle time increases, Reρ and the absolute values of Imρ of samples with vertical and parallel bedding structures both increase continuously. The increased amplitude becomes gradually smaller, especially in the frequency band below the fp of Reρ and near the fc of Imρ. The fp and fc gradually decrease, and the dispersion degree (α) of the dispersion curve gradually increases. This fracturing technology has a good effect on enhancing the permeability and expanding capacity of coal. While the fracture structure of coal continuously expands, it also changes the electrical performance of coal. Compared with the changes in coal electrical properties during multiple cycle times, the changes in coal electrical parameters in the first 12 cycles are larger, indicating that the fracturing effect in the early stage is significantly better than that in the later stage. This also indirectly indicates the limitations of liquid nitrogen cyclic freeze–thaw fracturing technology to a certain extent.

Table 3. Complex Resistivity Characteristic Parameters of Sample Va under Different Cycle Times.
cycle times Reρf=1/kΩ·m ΔReρf=1/kΩ·m fp/Hz Imρmin/kΩ·m ΔImρmin/kΩ·m fc/Hz dispersion degree (α)/%
0 10.725   40.754 4.542   266.62 97.796
4 18.28 7.555 18.672 8.134 3.592 143.33 99.674
8 23.528 5.248 10.398 10.535 2.401 116.55 99.732
12 26.311 2.783 7.038 11.601 1.066 94.767 99.738
16 27.975 1.664 5.79 12.278 0.677 77.056 99.778
20 29.053 1.078 5.79 13.06 0.782 77.056 99.808
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Table 4. Complex Resistivity Characteristic Parameters of Sample Pa under Different Cycle Timesa.
cycle times Reρf=1 ΔReρf=1/kΩ·m fp/Hz Imρmin/kΩ·m ΔImρmin/kΩ·m fc/Hz dispersion degree (α)/%
0 6.065   495.95 2.546   2110.4 97.382
4 11.582 5.517 216.79 5.039 2.493 1395.3 97.748
8 15.475 3.893 143.33 6.724 1.685 1134.6 98.234
12 17.749 2.274 94.767 7.621 0.897 922.54 98.567
16 19.486 1.737 77.056 8.147 0.526 750.13 98.592
20 20.756 1.27 77.056 8.448 0.301 750.13 99.095
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a

Notes: Inline graphic, Imρmin is the value of the characteristic frequency point of the Imρ curve, kΩ m; Imρmax is the maximum value of the Imρ curve, that is, the value of the highest frequency of the Imρ curve (200 kHz), kΩ m.

The reason for the cycle time effect of complex resistivity parameters is as follows. The mechanism of liquid nitrogen freeze–thaw technology is mainly influenced by the freeze–thaw force of water–ice phase transition.69 Specifically, under low temperatures, the liquid water in coal voids freezes into solid ice, and the volume expansion increases by 9%, resulting in an expansion pressure of 207 MPa at the tip of the coal fracture, causing the fracture to crack.70 Under the siphoning effect, the free water inside the coal migrates, increasing the volume of the ice prism and leading to the continuous development of coal fractures; Under the action of freeze–thaw expansion force, unfrozen water inside the coal also generates a certain degree of pressure, which contributes to the development of fractures. In addition, there is also the effect of the vaporization expansion force of liquid nitrogen.71 Heat exchange occurs between liquid nitrogen and coal, and liquid nitrogen absorbs heat and heats up. Eventually, the phase change occurs, and vaporization occurs, causing a rapid expansion of the volume and generating a huge nitrogen pressure. Under normal pressure, liquid nitrogen at −196 °C vaporizes and expands into pure liquid nitrogen at 21 °C, with a volume increase of 696 times, thereby expanding the fractures in the coal. There is also thermal stress generated inside the coal due to the injection of liquid nitrogen, and the phenomenon of the thermal stress concentration is more significant at the particle interface or grain boundary. When the thermal stress exceeds the tensile strength limit of the coal, it causes microscopic damage to the coal.72 When liquid nitrogen freeze–thaw acts on coal containing water, the water–ice phase transition frost heave force is the main mechanism of action. Cyclic fracturing is the result of the coupling of cumulative damage to coal based on the water–ice phase transition and gas fracturing. The repeated alternation of cold and heat gradually weakens the mechanical strength of coal, leading to the generation of new fractures and the extension of existing fractures as well as the separation of some mineral components. However, this transformation effect on the fracture structure of coal continuously weakens with an increase in fracturing times.

The Reρ and Imρ of coal are the real and imaginary components of its own complex resistivity, both of which characterize its electrical properties, corresponding to changes in its own fracture structure. As the fracture structure of coal increases, the distance between its functional groups and adjacent molecules gradually increases, the cross-linking between molecules decreases, the spacing between aromatic stripes increases, and the contact distance between conjugated electron pairs on the aromatic ring also gradually increases. The number of electron transfers between molecules decreases, and the electron transfer rate decreases.73 It becomes more difficult for the captured-state electrons within the functional group to be excited as free-state electrons;74 the captured-state electrons require more energy for transition and are more difficult to complete. The number and concentration of free radicals gradually decrease, the displacement polarization and the molecular-induced electric moment become weaker, and the electric dipole moment vector per unit volume decreases, resulting in a decrease in the conductivity of coal; that is, the Reρ and the absolute value of Imρ both increase. In addition, under the action of liquid nitrogen freezing and thawing, the detachment and loss of conductive minerals directly damage the effective conductive channels of coal, resulting in an increase in Reρ and the absolute value of Imρ. Due to the increase in the size of coal fractures, the migration distance of charged particles in the coal increases and the time period required for anions and cations to complete polarization is longer, which means that the loading frequency supplied needs to be smaller to ensure full polarization. Therefore, the fp and fc of the coal decrease with the cracking of the coal. The absolute value of Imρ in fractured coal is greater than that in nonfractured coal, and the performance of the frequency band near fc of Imρ is more prominent, with almost no difference in the high-frequency range. The Imρ dispersion degree of coal indicates that the fracture structure of coal determines the speed of polarization completion time and the quality of the completion effect.

As the freeze–thaw cycle time increases, the freeze–thaw force of the water–ice phase transition and the vaporization of low-temperature liquid nitrogen form high-pressure nitrogen gas, which forms a gas–liquid two-phase flow with liquid nitrogen. The cycle acts on the tip of the coal fracture, causing the coal fracture to continuously expand. A nonfreezing water film exists at the interface between solid ice and coal matrix in the frozen coal in the early stage of fracture water freezing. Some water molecules are squeezed out and released at this weak point. The frost heave force of the coal does not increase compared to before, and it decreases exponentially with the increase in cracking frequency.18 Therefore, the increase in the fracture structure of coal is more pronounced in the early stage of cyclic fracturing and gradually decreases in the later stage of fracturing. Correspondingly, Reρ and the absolute value of Imρ of coal increase continuously with the increase of the number of cycles, but their increase gradually decreases. The numerical changes in fp, fc, and the dispersion degree of coal also decrease accordingly (see Figure 12).

Figure 12.

Figure 12

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Dispersion curve of complex resistivity with different bedding directions of coal samples in the 16th cycle time.

Figure 11.

Figure 11

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Dispersion curve of complex resistivity with different bedding directions of coal samples in the eighth cycle time.

3.2.2. Effect of Different Bedding Directions on the Dispersion Characteristics of Coal Complex Resistivity

Due to the heterogeneity of coal, the fracturing effect on coal in different bedding directions varies. Therefore, a comparative analysis was conducted on the dispersion characteristic curves of samples in different bedding directions, after they were subjected to the initial, 8th, 16th, and 20th cycle time treatments, as shown in Figures 10–13.

Figure 10.

Figure 10

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Dispersion curve of complex resistivity with different bedding directions of coal samples in the initial state.

Figure 13.

Figure 13

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Dispersion curve of complex resistivity with different bedding directions of coal samples in the 20th cycle time.

At any cycle time, the Reρ dispersion curve of coal samples in the vertical bedding direction is shifted to the left compared to the parallel bedding. The fully polarized frequency of the former is smaller than that of the latter. Within the frequency range below the fp, Reρv > Reρp. The variation of Reρ in the former between adjacent cycle times is greater than that in the latter. For Imρ, the dispersion curve in the vertical bedding direction is shifted to the left compared to that of the parallel bedding. The characteristic frequency of the former is smaller than that of the latter; within the frequency range near the fc, |Imρv| > |Imρp|. The variation of |Imρ| in the former is greater than that in the latter, and the dispersion degree of coal samples in the vertical bedding direction is greater than that in the parallel bedding. As the cycle time increases, the variation of Reρ and Imρ, as well as the difference in the dispersion degree between vertical and parallel bedding planes gradually decrease.

The reason for the anisotropy of complex resistivity during liquid nitrogen cyclic freeze–thaw fracturing is as follows. When the conductive carriers migrate in the vertical bedding direction, they need to overcome the “local potential barrier” generated by the mutual attraction between macromolecular structures and the “penetrating potential barrier” generated by the parallel stacking structure of the macromolecules. However, the conductive carriers in the parallel bedding direction do not need to overcome the “penetrating potential barrier”. The conductivity perpendicular to the aromatic layer is weaker than that parallel to the aromatic layer, and the potential difference in the former is greater than that in the latter. Therefore, the Reρ and |Imρ| of coal in the vertical bedding direction are greater than those in the parallel bedding direction, and the dispersion degree of Imρ in the former is greater than that in the latter. The movement of conductive interceptors of coal in the vertical bedding direction requires more energy and takes more time to complete polarization than in the parallel bedding direction, and the sufficient completion of the differentiation and migration of charged particles requires a loading frequency lower than that of parallel bedding; therefore, the fp and fc of the former are both lower than those of the latter. The fracturing effect of coal in the vertical bedding direction is better than that in the parallel bedding direction. The changes in fracture volume and surface area of the former are greater than those of the latter. Correspondingly, the amplitude of its electrical response characteristics follows a corresponding pattern; that is, the changes in the Reρ, Imρ, and dispersion degree of the former are greater than those of the latter. Under the triple mechanical mechanisms of freeze-induced cracking, expansion-induced cracking, and low-temperature-induced cracking generated by liquid–gas phase transition and water–ice phase transition during the injection of liquid nitrogen into coal, fatigue damage and failure occur in the coal. The degree of bonding of weak planes in the internal bedding structure of the coal is more easily weakened, and the fractures in the coal gradually develop. As the cycle time increases, the degree of development and cross-connectivity of coal fracture structures gradually increases. The control effect of the coal bedding structure on coal power performance gradually weakens, and the differences in bedding properties such as Reρ, Imρ, and dispersion degree of coal also gradually decrease. Moreover, the bedding structure of coal can be equivalent to a circuit system composed of electronic components. When the direction of the external excitation electric field is parallel to the vertical bedding direction of coal, the coal sample can be regarded as a circuit composed of multiple resistors connected in series; similarly, when the direction of the external excitation electric field is parallel to the parallel bedding direction of the coal, the coal sample can be regarded as a circuit composed of multiple resistors connected in parallel. Obviously, the total resistance of a series circuit with resistors is greater than that of a parallel circuit, and each resistor increases by the same resistance value; the resistance change of the series circuit is greater than that of the parallel circuit. Therefore, the resistance value of coal in the vertical bedding direction is greater than that of coal in the parallel bedding direction, and the amplitude of the change also follows the same pattern.

3.3. Effect of Liquid Nitrogen Cyclic Freeze–Thaw on the Seepage Characteristics of Coal

3.3.1. Effect of Different Cycle Times on the Seepage Characteristics of Coal

Coal permeability depends on multiple factors such as confining pressure, axial pressure, pore pressure, and flow rate. To simplify and clarify the evolution process of coal permeability under the action of liquid nitrogen cyclic freeze–thaw, the parameter of effective pressure is introduced, and its calculation expression is shown in eq 3.

3.3.1. 3

Notes: σe is the effective pressure, MPa; σa is the axial pressure, MPa; σb is the confining pressure, MPa; p1 is the inlet pressure, MPa; and p2 is the outlet pressure, MPa.

The variation trends of coal permeability with cycle time under the same pore pressure, same confining pressure, and equal gradient axial pressure conditions are shown in Figures 14 and 15.

Figure 14.

Figure 14

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Permeability variation curve of coal samples in the vertical bedding direction with different cycle times.

Figure 15.

Figure 15

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Permeability variation curve of coal samples in the parallel bedding direction with different cycle times.

As seen from Figures 14 and 15 and Tables 5–8, the permeability of coal in the vertical and parallel bedding directions remains consistent with different cycle times. At the same number of cycle times, the permeability of coal samples decreases continuously with the increase in effective pressure, and the magnitude of the decrease gradually decreases. The average decrease in permeability of vertical bedding coal is −0.00167, −0.00127, −0.00067, and −0.00045 mD, while the average decrease in permeability of parallel bedding coal is −0.00131, −0.00095, −0.00054, and −0.00034 mD. Under the same effective pressure, as the number of cycle times gradually increases, the permeability of coal continuously increases, and the amplitude of the increase gradually decreases. The average increase in permeability of vertical bedding coal is 0.00198, 0.00179, 0.00147, 0.00093, and 0.00074, while the average increase in permeability of parallel bedding coal is 0.00148, 0.00136, 0.00129, 0.00087, and 0.00068 mD (see Table 6).

Table 5. Reduction in Permeability of Sample Va under Different Effective Pressures.
effective pressure/MPa 0 4 8 12 16 20 average
1.48              
1.645 –0.00047 –0.00112 –0.00181 –0.00197 –0.00226 –0.00237 –0.00167
1.81 –0.00031 –0.00079 –0.00116 –0.00156 –0.00188 –0.00194 –0.00127
1.975 –0.00019 –0.00032 –0.00045 –0.00089 –0.00105 –0.00114 –0.00067
2.14 –0.00011 –0.0002 –0.0003 –0.00056 –0.00065 –0.0009 –0.00045
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Table 8. Increase in Permeability of Sample Pa under Different Cycle Times.
cycle time 1.48 MPa 1.645 MPa 1.81 MPa 1.975 MPa 2.14 MPa average
0            
4 0.00202 0.00154 0.00137 0.00126 0.00122 0.00148
8 0.00211 0.0017 0.00125 0.00095 0.00079 0.00136
12 0.00171 0.00142 0.00128 0.0011 0.00096 0.00129
16 0.00103 0.00103 0.00093 0.00078 0.00062 0.00087
20 0.00072 0.00066 0.00068 0.00072 0.00063 0.00068
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Table 6. Increase in Permeability of Sample Va under Different Cycle Times.
cycle time 1.48 MPa 1.645 MPa 1.81 MPa 1.975 MPa 2.14 MPa average
0            
4 0.00286 0.00221 0.00173 0.0016 0.00151 0.00198
8 0.00264 0.00195 0.00158 0.00145 0.00135 0.00179
12 0.00207 0.00191 0.00151 0.00107 0.00081 0.00147
16 0.00144 0.00115 0.00083 0.00067 0.00058 0.00093
20 0.00095 0.00084 0.00078 0.00069 0.00044 0.00074
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Table 7. Reduction in Permeability of Sample Pa under Different Effective Pressures.
effective pressure/MPa 0 4 8 12 16 20 average
1.48              
1.645 –0.00048 –0.00096 –0.00137 –0.00166 –0.00166 –0.00172 –0.00131
1.81 –0.00041 –0.00058 –0.00103 –0.00117 –0.00127 –0.00125 –0.00095
1.975 –0.00012 –0.00023 –0.00053 –0.00071 –0.00086 –0.00082 –0.00054
2.14 –7 × 10–5 –0.00011 –0.00027 –0.00041 –0.00057 –0.00066 –0.00034
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The reason for the above trend is that the increase in effective pressure causes the internal fracture structure of coal to shrink and close, leading to a gradual reduction of methane seepage channels, continuous decrease in the average molecular free path of seepage gas, continuous increase in the resistance of gas passing through coal, and decrease in the overall permeability of coal. The deformation process of coal can be refined into these stages: “compaction stage-elastic stage-plastic stage-fracturing stage”. In order to discuss the law of multiple cycle times of liquid nitrogen fracturing, the effective pressure of the coal permeability test only puts coal in the compaction stage. The compressive performance of coal in the early stage of compression is inferior to that in the later stage, and the shrinkage deformation amplitude of coal fractures in the early stage is greater than that in the later stage. Therefore, the decrease in the permeability of coal gradually decreases with the increase in effective pressure. As the cycle time increases, frost heave force and thermal force are repeatedly generated under the action of cold and hot alternation. Small fractures continue to develop and connect, resulting in larger-sized fractures, which then develop into microfractures and macroscopic fractures. Some mineral components of coal gradually fall off, contributing to the increase in the number of fractures. However, as the cycle time increases, the peak frost heaving force gradually decreases. Therefore, the average growth of fractures slightly decreases with an increase in cycle times. The improvement effect of liquid nitrogen freeze–thaw cycle times on the permeability decreases, indicating that the promotion effect of cycle times is limited.23

3.3.2. Effect of Different Bedding Directions on the Seepage Characteristics of Coal

The anisotropic characteristics of coal make its permeability sensitive to the bedding direction. Based on the measured permeability data, the differential permeability changes of coal in different bedding directions are plotted under the same effective stress conditions for the initial, 8th, 16th, and 20th fracturing cycle times, as shown in Figure 16.

Figure 16.

Figure 16

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Permeability curves of coal samples with different bedding directions.

By comparing and analyzing the permeability differences between the different bedding directions of coal, it is seen that, at the same number of fracturing cycles, the permeability of vertical bedding coal samples is lower than that of parallel bedding coal. Under the same effective pressure condition, the permeability of vertical bedding coal is inferior to that of parallel bedding coal. The permeability difference between the adjacent cycle time and adjacent effective pressure in coal samples with a vertical bedding direction is larger compared to the parallel bedding, but this difference gradually decreases with the increase in cycle times. The bedding direction has a great influence on the permeability. When the direction of the seepage gas is consistent with the bedding direction of coal, the flow of gas is better. As the angle between the bedding direction and the direction of gas migration gradually increases, the difficulty of gas passage through coal increases. The degree of porosity development of coal has a certain degree of interference effect on the permeability difference guided by the bedding. Specifically, the larger the porosity of coal, the smaller the anisotropy of coal permeability, which is similar to the anisotropy law of coal complex electricity.

In order to more intuitively characterize the fracturing effect, nondestructive CT scans were performed on the initial state of coal samples Va and Pa, as well as the state after the 20th fracturing cycle. More accurate research was conducted on the dynamic evolution law and morphological change of internal fractures in coal caused by freeze–thaw cycle times and bedding direction. In addition, CT scan information on 3D fracture structures fully reflecting the instability and damage of coal samples was obtained. Digital image processing was carried out on the scanned slices, and the VG Studio MAX image analysis software was used to reconstruct the three-dimensional model from CT scan data, resulting in the visualized digital coal core. This enabled accurate extraction and digital qualitative and quantitative characterization of fracture size and morphology.

In Figure 17, three gray levels can be clearly distinguished, where white represents the mineral composition of coal, gray represents the coal matrix, and black represents fractures. Compared to rocks, coal has strong heterogeneity. As seen from the comparative analysis of the above pictures, the number, length, aperture, surface area, and volume of fractures in the coal increase after the liquid nitrogen cyclic freeze–thaw, and the initiation and extension of fractures are mostly along the bedding direction. During the generation of some fractures, the filling mineral composition in coal is also reduced to a certain extent. The number of connection points between fractures increases, and the morphology of fractures gradually evolves from simple isolation to a complex connected network structure.

Figure 17.

Figure 17

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Two-dimensional scan slices of coal before and after liquid nitrogen freeze–thaw fracturing.

However, it is not enough to analyze the evolution law only from two-dimensional planar image information. It is necessary to combine a more appropriate comprehensive quantitative analysis of evolution characteristics of coal samples in three-dimensional space to accurately analyze their control effect on permeability. With VG Studio MAX image processing software, three-dimensional digital reconstruction was performed on CT images before and after freeze–thaw cycles to obtain a visual three-dimensional map, as shown in Figure 18. The data obtained during the reconstruction process were processed and integrated, as shown in Table 9.

Figure 18.

Figure 18

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Three-dimensional reconstruction model of coal before and after liquid nitrogen freeze–thaw.

Table 9. Fracture Parameters of Coal before and after Liquid Nitrogen Freeze–Thaw.
fracture parameter coal sample in vertical bedding
 coal sample in parallel bedding
  initial state 20th variation initial state 20th variation
aperture/mm 213.68 523.02 309.34 194.39 1144.67 950.28
length/mm 245.88 1044.73 798.85 221.66571 2288.7961 2067.13
surface area/mm2 3595.71 35157.8 31562.09 2574.56 26466.7 23892.14
volume/mm3 156.51 1551.44 1394.93 123.12 1462.9 1339.78
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The three-dimensional reconstruction model displays the volume difference of fractures in terms of magnitude. The color of the fractures in the figure changes from purple to green and then to red, representing a regular change in fracture size from small to large. The volume contribution rate of large fractures is dominant. After the coal undergoes fracturing, the fracture structure of coal significantly increases and the directional effect of bedding is strong, resulting in penetrating fractures in the direction of bedding. After the fracturing effect, the aperture of the vertical bedding increases from 213.68 to 523.02 mm, the length increases from 245.88 to 1044.73 mm, the surface area increases from 3995.71 to 35157.8 mm2, and the volume increases from 156.51 to 1551.44 mm3. The aperture of parallel bedding increases from 194.39 to 1144.67 mm, the length increases from 221.66571 to 2288.7961 mm, the surface area increases from 2574.56 to 26466.7 mm2, and the volume increases from 123.12 to 1462.9 mm3. These results indicate that the liquid nitrogen freeze–thaw treatment has a significant effect on the modification of fracture parameters such as fracture aperture, length, surface area, and volume of coal. As cycle time increases, the influence of the development of coal fractures on the permeability of coal gradually strengthens, while the anisotropy of coal gradually weakens.

In addition, the volume contributions of coal fractures under different bedding directions and different liquid nitrogen cyclic freeze–thaw conditions were quantitatively analyzed, as shown in Figure 19. Before fracturing, the vertical bedding coal samples are mostly characterized by fractures with an aperture greater than 30 mm, accounting for 54.26%. After fracturing, the contribution rate of fractures at this scale increases to 95.01%, while the contribution rates of fractures with apertures of 0–10, 10–20, and 20–30 mm all decrease. The contribution rate of fracture volume of parallel bedding coal samples with a fracture aperture of more than 30 mm before fracturing is 63.86%. After fracturing, the contribution rate of this fracture volume increases to 90.83%, while the contribution rate of fracture volume in other ranges of fracture apertures decreases. These results imply that the liquid nitrogen freeze–thaw fracturing technology transforms isolated small-sized fractures in coal into connected large-sized fractures. The damage forms of fractures are the generation of new fractures as well as the enlargement and widening of pre-existing fractures and are mainly guided by the bedding structure, forming a complex network of fractures.

Figure 19.

Figure 19

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Volume contribution rate of different-sized fractures in coal before and after liquid nitrogen freeze–thaw.

3.4. Sensitivity of the Complex Resistivity Characteristics of Liquid Nitrogen Freeze–Thaw Coal to Its Permeability Enhancement

Based on the above analysis, it can be concluded that the complex resistivity response of coal is highly sensitive to the effect of fracturing. As an inherent physical property parameter, the permeability of coal is influenced by its internal material composition and the complexity and directionality of fracture structure, which effectively demonstrates the changes in the fracture structure of coal under the action of fracturing. The electrical and permeability properties of coal were linked, and a method for evaluating the enhancement effect of liquid nitrogen cyclic freeze–thaw was established based on a complex resistivity method.

According to the experimental measurements of the complex electrical parameters Reρ and Imρ, as well as the permeability k, as the cycle time of fracturing increases, Reρ and |Imρ| of coal gradually increase and the amount of change gradually decreases. The average permeability k value of coal also gradually increases, and the amount of change gradually decreases. This is attributed to the promotion effect of the fracturing technology on the transformation of coal fractures. However, this method of fracturing has a limitation as the conductivity of coal in the vertical bedding direction is weaker than that in the parallel bedding direction. Similarly, the permeability of the former is lower than that of the latter. The anisotropic characteristics of the complex electricity and permeability gradually weaken with the increase in cycle time, depending on the differences in the conductive channel and permeable channel in the different bedding structures. The increasingly complex fracture structure would also weaken the bedding characteristics of coal. Most researchers regard the polarization effect of the medium as the circuit and conduct electrical analysis on it. A mathematical model was calculated to invert the electrical information, and the dispersion characteristics of the medium under different reservoir conditions were explained through the parameters of the inversion model, further providing theoretical guidance for the electrical detection of coal fractures. These three models including the Debye model, Cole–Cole model, and Dias model (Table 10) were applied to invert and analyze the Imρ dispersion curve, as shown in Figure 20.

Table 10. Debye Model, Dias Model, and Cole–Cole Model Expressiona.

model expression
Debye model
graphic file with name ao4c04176_m007.jpg
Cole–Cole model
graphic file with name ao4c04176_m008.jpg
Dias model
graphic file with name ao4c04176_m009.jpg
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a

Notes: ρ(iω) is the measured complex resistivity value, kΩ·m; ρ0 is the zero-frequency complex resistivity value, kΩ·m; m is the polarization rate, the ratio of the overall amplitude of complex resistivity change to its maximum average value at low frequencies; c is the frequency correlation coefficient, representing the opening and closing shape of the curve to a certain extent, with a value range of 0 < c < 1; τ, τ1, and τ2 are the relaxation time constant, characterizing the speed at which coal completes the induced polarization, s.

Figure 20.

Figure 20

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Debye model, Dias model, and Cole–Cole model inversion on measured data.

The three electrical models provide similar curve trends for the measured data. The inversion accuracies of the Debye model, Dias model, and Cole–Cole model for the Imρ dispersion curves in the vertical bedding direction (parallel bedding direction) are 98.253% (98.809%), 98.405% (98.069%), and 99.899% (99.735%), respectively. Although the inversion accuracy of all three models is high, the Cole–Cole model has slightly higher accuracy compared with the first two models. The relative deviation between the inversion curve and the measured curve is smaller, especially near the characteristic frequency point, fc, which is more obvious. In addition, the Debye model does not have parameters to determine the degree of curve opening or closing. The Dias model has a large number of parameters, which increases the difficulty of data interpretation accuracy. However, the Cole–Cole model has a small number of parameters and clear physical meanings and can accurately reflect the trend and polarization characteristics of coal measurement data. Therefore, the Cole–Cole model was selected as the complex electrical inversion model for liquid nitrogen cyclic freeze–thaw of coal, and the inversion results are shown in Figure 21 and Tables 11 and 12.

Figure 21.

Figure 21

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Inversion curves of the Cole–Cole model with different cycle times and different bedding directions.

Table 11. Cole–Cole Model Inversion Parameters in the Vertical Bedding Direction.

cycle time ρ0/kΩ·m m c τ/s
0 11.363 0.95395 0.90185 5.39512 × 10–4
4 19.326 0.95151 0.92318 1.03 × 10–3
8 25.072 0.95908 0.91562 1.37 × 10–3
12 28.097 0.96109 0.9045 1.56 × 10–3
16 30.054 0.93527 0.91506 1.71 × 10–3
20 31.365 0.93742 0.92603 1.81 × 10–3
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Table 12. Cole–Cole Model Inversion Parameters in the Parallel Bedding Direction.

cycle time ρ0/kΩ·m m c τ/s
0 6.123 0.90868 0.93571 9.09005 × 10–5
4 12.103 0.94049 0.92086 1.27372 × 10–4
8 16.265 0.94595 0.91078 1.52473 × 10–4
12 19.593 0.87422 0.92052 1.71787 × 10–4
16 21.076 0.94467 0.86667 1.87337 × 10–4
20 21.567 0.92684 0.88955 1.89888 × 10–4
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As seen from the above figure and table, the inversion curve of the Cole–Cole model is highly consistent with the measured data curve. Moreover, the response law of its model parameters to the cycle times shows that the values of model parameters m and c exhibit irregular and disordered fluctuations with the increase in cycle times. The values of model parameters ρ0 and τ gradually increase with the increase in cycle times, and the increased amplitude gradually decreases. The ρ0 and τ values for the vertical bedding direction coal sample are greater compared to the parallel bedding direction, and the former has a greater amplitude of change than the latter. This regular change is consistent with the measured data and mechanism analysis in the previous text. It reflects the electrical changes of coal under the action of fracturing and also fundamentally characterizes the polarization properties of coal. Therefore, after optimizing the model parameters ρ0 and τ as complex electrical advantage parameters for evaluating the freeze–thaw effect of liquid nitrogen, the value was compared and analyzed with the permeability of coal, as shown in Figure 22.

3.4. 4

Figure 22.

Figure 22

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Relationship among the complex electrical advantage parameters ρ0 and τ and permeability k of coal samples in different bedding directions.

Notes: ρ0 is the zero frequency complex resistivity value, which is the Cole–Cole model inversion parameter, kΩ·m; k is the permeability, mD; ε and γ are the model fitting parameters.

3.4. 5

Notes: τ is the relaxation time constant, which is the Cole–Cole model inversion parameter, s; k is the permeability, mD; and λ and σ are the model fitting parameters.

As shown in the above figure, there is good correspondence between the model inversion parameters ρ0 and permeability k, as well as τ and permeability k with different cycle times and different bedding directions. Specifically, as the cycle time increases, the values of k, ρ0, and τ gradually increase, and the magnitude of the increase varies from large to small. Under any number of fracturing cycles, the values of ρ0 and τ for the coal sample in the vertical bedding direction are all greater compared to the parallel bedding direction, while the k value in the former is smaller compared to the latter. There is a good logarithmic relationship between the model inversion parameters ρ0 and permeability k, as well as between τ and permeability k, as shown in eqs 4 and 5. In summary, the model parameters ρ0 and τ can predict the permeability of coal modified by liquid nitrogen freeze–thaw fracturing technology to a certain extent and further evaluate the effect of liquid nitrogen cyclic freeze–thaw fracturing.

4. Conclusions

In this work, the dispersion characteristics of complex resistivity and permeability changes of anisotropic coal under different fracturing conditions are summarized, and their correlation is discussed. The main conclusions are as follows:

  • (1)

    The Reρ and Imρ of coal are dependent on the frequency. As the frequency increases, the Reρ continuously decreases, and the decreasing rate changes from gradually accelerating to gradually slowing down, forming a slide shape. The Imρ value is negative, which first decreases at a continuously increasing decrease rate, then converts to a numerical increase, and the increasing rate gradually decreases, forming a valley shape. The conversion frequencies of the Reρ and Imρ curves correspond to each other.

  • (2)

    The dispersion response characteristics of coal complex resistivity can provide feedback on the effectiveness of liquid nitrogen cyclic freeze–thaw treatment. Reρ, |Imρ|, and α are positively correlated with cycle time; fp of Reρ, fc of Imρ, and variation are negatively correlated with cycle time. The promotion effect of cycle time on fracture reconstruction is limited. The molecular interval and contact distance of conjugated electron pairs on the aromatic ring of fractured coal gradually increase, conductive minerals gradually disappear, polarization completion time is prolonged, and effective conductive channels are destroyed.

  • (3)

    The dispersion characteristics of coal complex resistivity exhibit differences according to the bedding structure. Reρ, |Imρ|, variation, and α in the vertical bedding direction are greater compared to that in the parallel bedding direction. The fp and fc of the former are smaller than those of the latter. The difference in frequency dispersion between vertical and parallel bedding gradually decreases with the increase in cycle time. The migration process of charged particles in coal in the vertical bedding direction requires more energy and more time to complete polarization. The development degree and cross-connectivity of the coal fracture structure gradually increase, the control effect of the bedding structure on coal electrical properties gradually weakens, and the variation of electrical parameters gradually decreases.

  • (4)

    The complex electrical characteristic of liquid nitrogen freeze–thaw fractured coal is sensitive to its permeability enhancement. As the cycle time increases, the permeability of coal gradually increases and the amount of change gradually decreases. Reρ and Imρ of coal have a consistent pattern of change. There is a good logarithmic function between optimizing Cole–Cole model parameters ρ0 and k, as well as model parameters τ and k. Using CT scanning technology, the fracturing effect of coal in different bedding directions can be determined more intuitively and accurately, which also verifies the correctness of the law between complex electrical characteristics and permeability of coal under liquid nitrogen freeze–thaw technology.

The complex resistivity method is based on the dispersion characteristics of the coal reservoir’s electrical properties. The complex resistivity parameters of coal were measured under multiple frequency loads. Through the intermediate bridge “complex electrical resistivity dispersion characteristics”, a relationship model was established with the permeability of liquid nitrogen freeze–thaw fractured coal seams to achieve a correlation between electrical parameters and physical parameters. This work provides a theoretical basis for using a noninvasive identification technology to achieve rapid and real-time evaluation of changes in permeability during liquid nitrogen cyclic freeze–thaw fracturing of coal and experimental support for efficient development of CBM.

Acknowledgments

We are grateful for financial support of the research from the National Natural Science Foundation of China (2016ZX00504007-007), National Natural Science Foundation of China (41904118), Open Research Fund of the Key Laboratory of “Structure and Oil and Gas Resources” of the Ministry of Education (TPR-2019-05), Projects of Talents Recruitment of GDUPT, and Projects of PhDs’ Start-up Research of GDUPT (XJ2023000602).

The authors declare no competing financial interest.

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