Linlin Huang,Xiangjun Liu,Sen Yan,Jian Xiong,Haiming He,Peng Xiao

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Southwest Petroleum University,Chengdu,China

Keywords:Upper permian xuanwei formation Coal Acoustic wave propagation Frequency spectrum characteristics Anisotropy

ABSTRACT In order to study the propagation laws of acoustic wave of coal samples from the Upper Permian Xuanwei Formation in the east of Yunnan Province,China,under saturated water and dry conditions,the basic physical parameters,acoustic parameters and anisotropic parameters were obtained through the experiments.Based on FFT and wavelet analysis theory,the spectral characteristics of coal samples under different conditions were studied.The results show that physical parameters of coal samples in different directions have different values,that is,the anisotropy of coal samples is obvious.When the coal samples are saturated with water,the acoustic velocities and the attenuation coefficient increase,whereas the dominant frequency decreases.The signal amplitude of the frequency domain significantly decreases,that is,the internal structure of coal samples is damaged.The P-wave velocity and S-wave velocity increase with the increase of the confining pressure,whereas the anisotropy parameters decrease with the increase of the confining pressure.Overall,this study provides the basis to understand basic acoustic information and anisotropy characteristics of coal samples.

1.Introduction

With the increase of global energy demands and the continuous progress of exploration and development technologies,unconventional energy sources (including tight gas,shale gas,oil-bearing shales and coalbed methane,etc.) have shown great development potential under the current economic and technological conditions [1–4].As a kind of unconventional energy,coalbed methane (CBM) is stored in coal rocks in an adsorbed form.Compared with conventional reservoirs,the coals have the characteristics (e.g.,cleat development,wide pore size distribution and complex internal pore structure) [5,6],which result in increased difficulties in exploration and development of coalbed methane.As an information carrier,acoustic wave carries abundant rock physical and mechanical information when it propagates in rock strata,which reflects the internal structural characteristics of rock and rock mass.It has been widely used in the research of physical and mechanical properties of all kinds of rock and rock mass [7–9].Therefore,the study of acoustic characteristics and anisotropy of coal rocks is of great significance to the exploitation of coalbed methane.

At present,some researchers have studied the anisotropic characteristics of rocks,including velocity anisotropy [10–13],stress anisotropy [14,15],elastic anisotropy [16,17]and mechanical anisotropy [18,19]and so on.Matonti et al.[11]and Wang et al.[12]analyzed the relationships among P-wave velocity and S-wave velocity,inclination,axial stress by means of the ultrasonic pulse transmission technique.Ji et al.[13]concluded the relationships between P-wave velocity anisotropy and pressure.Tak et al.[14]used full azimuth seismic and well data to investigate the horizontal stress anisotropy.Sayers et al.[16]used the normal compliance and shear compliance to represent the interlayer regions in clay minerals,and investigate the relationships among Thomsen’s anisotropy parameters,the normal compliance and shear compliance.Zhao et al.[18]analyzed the anisotropy of coals using experimental and numerical methods.Wang et al.[20]carried out the experiments to investigate the anisotropy of the thermal,hydraulic,and mechanical characteristics of oil shale.These studies indicate that scholars have done a lot of researches on the anisotropy characteristics of different types of rocks (shale,carbonate,coal,etc.) and obtained some understanding.However,there are few studies on the anisotropic acoustic of coal rocks.Xiong et al.[21]investigated the relationships among the interval transit time,the attenuation coefficient and the bedding angle by experimental tests and numerical simulation.Shen et al.[22]analyzed the law of amplitude-frequency characteristics and frequency domain of acoustic emission signals under various water pressure by experiments.Du et al.[23]investigated systematically the laws of the acoustic emission signals during deformation by means of conventional triaxial compression.

Fig.1.Coal.

The mission of this paper is to investigate the acoustic propagation and anisotropy of coal rocks from the Upper Permian Xuanwei Formation in the east of Yunnan Province.Under the dry and saturated conditions,the ultrasonic pulse velocity test was used to obtain the parameters of the acoustic wave velocity,attenuation coefficient and main frequency of the coal samples.Based on the FFT theory,the frequency domain data was obtained,and the wavelet transform was used to further study the micropore structure change characteristics of the coal samples after being saturated with water.On this basis,the influence of confining pressure on acoustic wave propagation characteristics and anisotropy of coal rocks were discussed.

2.Samples and methods

The coal samples used in the experiment were collected from the eastern Yunnan area,where most of the coal seams can be mined stably.Considering that the coal sample is easy to be damaged in the preparation process,the raw coal block with side length not less than 200 mm is preferred in the coal sample collection process to observe the structural characteristics of the coal block.

2.1.Samples

According to the statistical analysis of field sampling,the coal rocks in the eastern Yunnan area have a bright appearance,which are mainly semi-bright briquette and semi-dark briquette,and contain a small amount of dim briquette.And the coal structure is mainly composed of primary structure and cataclastic structure,with a very developed cleat system.Besides,the structure is broken,and the cleat occurrence is observed obviously.(Fig.1).From Fig.1,it can be seen that both the face cleats and the butt cleats are distributed in the form of short cracks,and the extension range of the face cleat is longer than the butt cleat,with a length of about 1 mm–40 mm,a width of about 0.008mm–0.4 mm,a face cleat of about 10–15/3 cm,and an butt cleat of about 10–19/3 cm [24].

Fig.3.Sampling direction and structure diagram of coal rock.

The microstructure of coal rocks mainly refers to the fracture structure developed in coal rocks,including the exogenous fracture caused by the structural stress of coal seam and the endogenous fracture (face cleat and butt cleat) produced in the process of coalification.The endogenetic fractures (face cleat and butt cleat) in coal rocks are the main fractures[24].In order to better understand the microstructure of coal rocks,the internal structure characteristics of coal rocks are observed by scanning electron microscope (Fig.2).From the scanning electron microscope,it can be seen that the cleats of coal rocks in the eastern Yunnan area are very developed,and the face cleats and the butt cleats are intersected and cut.

3.Methods

In order to study the anisotropic characteristics of coal samples,firstly,the coal blocks were processed and made into a 100 mm × 100 mm × 100 mm cube coal sample.The acoustic wave velocities of coal samples were measured along the adjacent three sides to obtain the direction of the maximum and minimum wave velocity.In this direction,the coal samples were drilled (separately recorded as X and Y directions),and the cores were taken in the X,Y and Z directions (Fig.3).The two ends were then ground smooth with a cutting machine to produce a standard cylinder with a diameter of 25 mm and a height of 50 mm.The diameter and height errors of coal samples shall be controlled within ±0.3 mm.The unevenness error of the two ends shall be less than 0.3 mm,so as to ensure that the end faces were parallel.In order to ensure the accuracy of anisotropic parameter measurement,samples with obvious cracks and end face falling off block were abandoned during sample preparation.

The drilled coal samples were placed at a constant temperature of 60°C to dry for 24 h,then put into a drying dish to cool to room temperature,and the basic physical parameters (including length,diameter,mass and porosity) were measured (Table 1).Ultrasonic transmission method was used to measure the acoustic characteristics of coal samples.The experimental devices include:computer,ultrasonic excitation,receiver,core gripper and oscilloscope,etc.During the experiment,vaseline was applied between the coal samples and the acoustic transducer.Based on the obtained acoustic waveform information and length L,the arrival time and system delay of the first wave of the longitudinal and transverse waves were read.Meanwhile,in order to ensure the accuracy of acoustics parameters,it is necessary to remeasure the acoustic arrival time before each set of measurements and take three readings and average them during the experiments.The acoustic wave velocity formula was used to calculate:

Table 1 Basic physical parameters of coal sample.

Table 2 Information of coal sample before and after water filling.

Fig.4.Acoustic waveform and frequency curve of some coal samples under dry and saturated water conditions.

where L is the length of coal samples,m;tp、tsare arrival time of the first wave of the longitudinal and transverse waves,respectively,s.tp0、ts0are system delay time of the first wave of the longitudinal and transverse waves,respectively,s.

In the experiment,firstly,the acoustic information of coal samples was measured under dry condition,then the rock samples were treated with saturated water.To make the coal samples fully saturated with water,firstly,the coal samples were vacuumized for 24 h and then placed in the original saturated solution for 12 h.The coal samples at this time were regarded as 100% saturated water.The weight and acoustic data of the coal samples were measured in time.In order to avoid the influence of external factors on the acoustic information collection of coal samples,a relatively stable position between the coal samples and the transducer was ensured during the measurement.

On the basis of recording the acoustic wave time domain signal of coal samples,the frequency domain signal of acoustic wave was obtained based on fast Fourier transform (FFT),and the acoustic wave spectrum characteristics of coal samples after water saturation were further studied.The acoustic signal obtained by experiment is a finite discrete digital signal,which requires finite discrete Fourier transform(DFT).However,there exists the problem of large computation,especially for the case of numerous sampling points.For this reason,Cooley and Tukey proposed a fast algorithm of DFT in 1965,which is called fast Fourier transform.We assume that there is a periodic signal x(T) with a period of 2 L.The discrete form of Fourier transform can be expressed as:

wherea0，ak，bkare Fourier coefficient;N is the transformation interval length;m is the sampling points.

In order to describe anisotropic parameters,some scholars put forward different theories.In this paper,physical quantities δ,γ,ε related to elastic constants proposed by Havens et al.[25,26]were selected to characterize the anisotropy characteristics of coal samples,and the relationships between the three quantities and the elastic coefficients of transversely isotropic media were given.The calculation formula of each parameter is:

Fig.5.Coefficient diagrams of continuous wavelet transform of some coal samples.(a) Sample x-1 under dry condition.(b) Sample x-1 of water-saturated.(c)sample y-1 under dry condition (d) sample y-1 of water-saturated.(e) Sample z-1 under dry condition.(f) Sample z-1 of water-saturated.

Fig.6.The variation of wave velocity of coal sample with confining pressure.

Fig.7.Variation of anisotropic parameters of coal samples with confining pressure.

The relationships between the rigidity coefficient and the density of coal samples and the velocity of acoustic wave:

whereCyare stiffness coefficients describing the physical characteristics of a medium;ρ is the density of sample,g/cm3;Vis acoustic velocity,km/s.

4.Results and discussions

4.1.Acoustic attenuation anisotropy characteristics of coal samples

The acoustic wave information before and after coal samples were saturated is presented in Table 2.It can be seen from Table 1 that the porosity of coal samples is generally small,and the saturation rate is also small.From Table 2,we observe that the longitudinal wave velocity of the dry coal sample ranges from 47.44 dB/m to 2459.48 m/s,with an average value of 2424.00 m/s,and the wave velocity is anisotropic,indicating that the internal structure development of the coal sample in different directions is different.The longitudinal wave velocity of coal samples increased by 32%–45% after the coal sample was filled with water,because the water occupied the corresponding storage space after entering the coal samples,which is consistent with Liu et al.[27]Under dry condition,the attenuation coefficient of coal samples is from 22.38 dB/m to 44.52 dB/m,with an average value of 34.27 dB/m.After the coal samples were filled with water,the attenuation coefficient increased significantly.The values of the attenuation coefficient are from 47.44 dB/m to 65.14 dB/m,with an average value of 55.69 dB/m.The results in different directions show that the acoustic characteristics of coal samples are various,indicating that coal samples have the anisotropic characteristics.

4.2.Waveform characteristics of coal samples under saturated and dry conditions

Influenced by the filtering effect of the propagation medium on the excitation signal and the absorption effect of the medium,the waveform of acoustic wave passing through the coal samples is significantly different [28].Based on FFT theory,the received time domain signals were converted into frequency domain signals,and the attenuation laws of coal samples were studied from two aspects,namely,time domain and frequency domain (Fig.4).

All coal samples show a decrease in waveform amplitude after water saturation.This may be because after the coal samples are filled with water,the internal pores are occupied by water,the superposition of reflection and refraction of sound waves is weakened [29].Meanwhile,the signal energy decreases obviously and the spectral energy is dispersed,indicating the coal samples have a strong absorption and attenuation effect on the high-frequency part of the sound wave after the coal sample is saturated.The main frequency of acoustic wave refers to the frequency corresponding to the peak of the largest spectrum in the frequency domain.Under the same excitation signal,the main frequency of the coal samples in the dry condition is much higher than that of saturated water,indicating that the main frequency of acoustic wave is more sensitive to the influence of water.

In order to deeply understand the changes of internal microscopic pore structure of coal samples after saturated water,the method of wavelet change was adopted for further study (Fig.5).From Fig.5,we can note that the dark areas of the wavelet transform coefficient of coal samples increase significantly after the coal samples are full of water,suggesting that the internal structure of coal samples is damaged.

4.3.Anisotropic characteristics of coal samples under different confining pressures

By applying a confining pressure of 10 MPa–40 MPa (with a spacing of 10 MPa),the relationships between the velocity of the longitudinal and transverse wave and the confining pressure are obtained (Fig.6).With the increase of confining pressure,the longitudinal and shear wave velocities continue to increase,whereas the confining pressure increases to 10 MPa,the wave velocity increase the fastest,with an average increases of 13.27% in longitudinal wave velocity and 19.60% in transverse wave velocity.When the confining pressure is greater than 10 MPa,the longitudinal and transverse wave velocities increase slowly.At the same time,it also can be seen from Fig.6 that after confining pressure is applied,the differences in the velocity of vertical and horizontal waves of coal samples in different directions decreases.This finding is agreement with the previous works on the shales [11,30,31].This may be because the pores and cracks in the coal sample are closed after confining pressure is applied.

The variation laws of elastic anisotropy parameters of coal samples with confining pressure can be seen in Fig.7.From Fig.7,we can observe that the values of each elastic anisotropy are relatively large,indicating that the coal samples show strong anisotropy.Besides,with the increase of confining pressure,the coefficient of elastic anisotropy decreases,which is consistent with previous studies on the shales [30,31]

5.Conclusions

(1) Under the same conditions,the water-filling capacity of coal samples in different directions of the same coal seam has obvious anisotropy.Compared with the dry condition,the wave velocities of coal samples increase after the water is saturated,the main frequency decreases,the energy of the high-frequency part of the acoustic signal decreases seriously,the energy of the lowfrequency part increases,and the attenuation coefficient obviously increases.

(2) After the acoustic wave is transmitted to the coal sample,the waveform is obviously distorted and the amplitude is obviously reduced.After the coal sample is saturated with water,the main frequency of the frequency curve is prominent,the attenuation degree of the high frequency part increases,and the low frequency develops.

(3) The coal samples are strongly anisotropic medium.With the increase of confining pressure,the elastic anisotropic parameters ε、γ、δ decrease.

CRediT authorship contribution statements

Linlin Huang:Experiment,Data analysis,Writing-Reviewing.Xiangjun Liu:Investigation.Sen Yan:Experiment,Data analysis,Writing-Reviewing.Jian Xiong:Investigation,Data analysis.Haiming He:Experiment.Peng Xiao:Experiment.

Acknowledgements

This research is supported by the Young Scientific and Technological Innovation Team of Rock Physics in Unconventional Strata of Southwest Petroleum University(No.2018CXTD13),the 19th issue college students’ Extracurricular opening experiment key projects,Southwest Petroleum University (No.KSZ19207),and Innovation and enterprise fund of School of Geoscience and Technology,Southwest Petroleum University(No.DCXP1930).