声波全波列测井的数值计算及其响应特征和时频分析
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摘要
声波全波列测井中包含着纵波、横波、伪瑞利波、斯通利波等不同性质的分波,这些分波的速度变化、幅度衰减、频率改变、频散效应等与井壁岩层的岩性、孔隙流体性质以及井眼条件等因素息息相关。因此,全波列测井当中蕴含着更多的地层信息。为此,本文对声波全波列进行了数值计算和分析,考察了不同性质地层中声波全波列的传播特征。
首先,本文根据井中声场理论,数值计算出了准弹性地层中的声场时域波形。利用数值计算出的二维谱分析了在软地层和硬地层两种不同地层中频率-波数域内波场的特征以及井径对声场传播的影响。
其次,为了考察孔隙介质中声场的传播特征,本文以Biot-Rosenbaum声场理论为基础,考虑动态渗透率的影响,引入动态渗透率的近似计算公式,数值计算出了饱和流体孔隙介质中的井孔声场全波列及其二维谱。详细分析了井孔中快纵波、慢纵波以及横波的频散、衰减系数变化等传播特征。
最后,本文利用Choi-Williams时频分析方法,求出了理论时域波形和实测声压波形Choi-Williams时频分布图,对比和分析了不同渗透率和含不同性质流体地层中声波传播的时频特征。
Full wave train in Acoustic Logging is a major breakthrough in the technological development of acoustic logging which makes a regular record of the sliding longitudinal wave (arrival time and amplitude) extended to the records of the sliding longitudinal wave and sliding transverse wave spreading along the wall of borehole and the records of the guided wave in the fluid in the wells between the borehole wall and the instrument’s shell in the pit. There are highly affluent in information about the properties and the characteristics of the wall of the well and stratum and the circumstance of borehole such as various types of wave velocity, amplitude and its attenuation, the change of frequency, the effect of frequency dispersion and the graphics of wave envelope and the like which are included in records. Therefore, in order to obtain these important stratum information, first, the velocity change, amplitude fading, frequency dispersion and otherwise of various partial wave included in full wave train must be considered to make sure that these characteristics have relations with which character of stratum, so we should study the characteristics of wave propagation in stratum with different properties. It is important to study the influence of stratum properties and borehole conditions on the wave propagation. Based on this idea mentioned above, in this paper, the author utilizes a computer to do the numerical calculation of the theory wave profile of wave acoustic logging, and uses the calculated two dimension spectrum combined with time-domain waveform to study and analyze the influence of the change of various stratum parameters to various partial waves in full wave train. In addition, for the sake of extracting more information from full wave train in acoustic logging, the author tries to do some analysis in time-frequency domain. Time-frequency analysis have been done to hole stratum containing fluids with different properties(oil layer, water layer) and the different permeability.
This paper mainly includes three parts. First, the research to the acoustic field propagation properties of elastic medium which includes wave propagation in soft and hard rock stratum and the hole diameter impacting on the acoustic field in the well. Second, the research of the acoustic field in porous media which mainly contains viscosity lag coefficient, permeability and the influence of the fluid properties (oil layer, water layer) make to the acoustic field. Third, the treatments of time-domain waveforms in the acoustic field in the well which mainly includes the comparison of time-frequency analysis methods and time-frequency characteristics of wave propagation in various stratums. The main contents are briefly described below.
In the first place, we see stratum as equivalent elastic formation that is quasi-elastic medium and don’t consider the influence of pore, so that acoustic model can be simplified and the solution of the acoustic field in the borehole can be obtained easily. Without regard to the stratum pore and the fluid contained, acoustic field calculated from quasi-elastic medium model can study and understand the influence which is caused by different properties stratum to the acoustic field better. Based on the theory of the 6 acoustic field in the well in this paper, time-domain waveform of the acoustic field in quasi-elastic stratum was numerical calculation. Two-dimensional spectrum numerical value is applied to analyze the character of two-dimensional spectrum in frequency– wave number domain in the soft stratum and hard stratum and the influence which is caused borehole radius to the acoustic field propagation. Through the two-dimensional spectral of soft stratum in contrast with two-dimensional spectral of hard stratum, and the analysis of character about longitudinal wave (first wave), transverse wave, mud longitudinal wave and phase velocity, group velocity and the change of chroma about two-dimensional amplitude of various model waves, we know that the phase velocity, group velocity of stratum longitudinal wave (first wave), stratum transverse wave, mud longitudinal wave change rarely in borehole acoustic field. Stratum transverse wave and the pseudo-rayleigh wave are not received in borehole axis in soft stratum. Leakage model corresponding to mode waves is a geometric decaying wave. It has the character of fast decay and stronger frequency dispersion in the acoustic field propagation. Transmission modes and characters of waves with the medium which have different properties were studied by two-dimensional amplitude spectrum of acoustic wave calculated in different medium condition.
In the second place, acoustic logging not only offer stratum lithology parameters, such as propagation velocity of longitudinal and transverse wave, but also provide reservoir parameters, such as the porosity, permeability and etc. Reservoir parameters have great significance for gas exploration, because oil gas and etc are stored in reservoir stratum of porous rock. Reservoir stratum is composed of solid phase skeleton. There is a mass of pore spaces which connect each other. Oil gas can store in it and flow oppositely. Mediums with this characteristic are called pore space mediums. Biot theory about the acoustic field propagation in pore space mediums has been widely recognized and applied and is recognized as the best theoretical model of the wave propagation in the description of pore space mediums at present. Pore space medium theory of Biot was applied to the research of acoustic logging by Rosenbaum(1974) for the first time. The influence of reservoir stratum parameters, such as porosity and permeability, on well borehole full acoustic wave information was studied numerically with point source model, and then he found that the permeability and stoneley wave had the closest relation which we called Biot-Roserbaum theory. The concept of the dynamic permeability was advanced by Johnson in 1987 and applied in Biot theory, and an approximate formula of dynamic permeability was given.
In this paper, borehole acoustic field two-dimensional spectrum in saturated fluid porous media was figured out numerically based on Biot-Rosenbaum acoustic wave theory numerical model, the consider of the influence of dynamic permeability and the introduction of approximate computational formula of dynamic permeability. By the use of Biot-Rosenbaum theory numerical model with the consider of the influence of dynamic permeability, fast longitudinal wave, slow longitudinal wave and frequency dispersion curves of transverse wave were calculated, and theoretical acoustic pressure waveform received in a point of well-axis with the given stratum condition was calculated and its two-dimensional spectrum was obtained. Stoneley wave, pseudo-rayleigh wave, longitudinal mode waves, transverse mode waves and the change character of the longitudinal and transverse wave in the condition of different permeability stratum can be seen clearly and directly through the calculated result of borehole acoustic field two-dimensional spectrum and the acoustic pressure waveforms chart in different permeability stratum.
The character of frequency dispersion of fast longitudinal wave, slow longitudinal wave and transverse wave were summarized through calculated frequency dispersion curves based on Biot-Roasenbaum theory numerical model with the consider of with the consider of the influence of dynamic permeability. Fast longitudinal wave and transverse wave has weak frequency dispersion, and the slow longitudinal wave has stronger frequency dispersion. The frequency dispersion of fast longitudinal wave weakened slightly and its speed increased slightly with the increasing of permeability. The frequency dispersion of slow longitudinal wave is strong. it weakened slightly with the increasing of permeability while the speed of the slow longitudinal wave increased evidently. The frequency dispersion of transverse wave weakened while its speed increased faintly with the increasing of permeability.
It can be seen from the calculated two- dimension spectrum that, in the frequency-wave number domain, two-dimensional spectral values has multiple culminating point, each culminating point correspond to the peak value of two-dimensional spectrum, and the peak values of two-dimensional spectrum are distributed in scaly structure in the two-dimensional spectrum. Sundry mode waves correspond to the peak and change with the change of stratum parameters. With the increasing of penetration, the two-dimensional spectrum values and the contribution of pseudo-rayleigh wave decrease relatively, while the contribution of leak mode waves to which longitudinal wave and transverse wave correspond enlarge relatively. As a result, the aggrandizement of permeability makes the losing energy of acoustic field in the geometric attenuation increase. The contribution of pseudo-rayleigh wave and the contribution of leak mode waves which longitudinal wave and transverse wave correspond to decrease relatively. As a result, the aggrandizement of permeability makes the losing energy of acoustic field in the geometric attenuation decrease.
By calculating the acoustic field two-dimensional spectrum and time domain wave column of oil layer and water layer, it can be seen that the contribution of transverse wave and pseudo-rayleigh wave of acoustic wave in oil-bearing formation is bigger than in water bearing ground and the energy of transverse wave and pseudo-rayleigh wave is higher. The contribution of stoneley wave in oil-bearing medium become smaller than water bearing ground, the amplitude and energy of stoneley wave is on the small side.
In this paper, the property of stoneley was studied importantly through two-dimensional spectrum and acoustic pressure waveform chart. It can be seen clearly from acoustic field two-dimensional spectrum in well with the condition of different permeability stratum that the speed of stoneley wave is slightly lower than the speed of the fluid in the well bore. Its frequency dispersion is weak. It has cutoff frequency and the frequency range is lower. Its size is between zero and cutoff frequency. Stoneley wave is sensitive about the change of permeability. The frequency range and amplitude attenuation of stoneley wave were effected by permeability. The amplitude of stoneley attenuates more tempestuously and the cutoff frequency of stoneley are smaller with its frequency range lower when the permeability is bigger. Stoneley wave is sensitive about the change of coefficient of viscosity. The amplitude attenuation of stoneley wave will be smaller and the frequency range of stoneley wave will be bigger while coefficient of viscosity is bigger. Through the study of acoustic field two-dimensional spectrum in the well bore in permeability stratum, we find that stoneley wave is sensitive about the change of permeability and coefficient of viscosity. Its frequency range and amplitude attenuation are influenced by permeability.
Third, in order to extract more information from full wave train in acoustic logging, the author tries to get more information in time-frequency domain. Several used commonly methods of time-frequency analysis are compared. A kind of Choi-Williams distribution of Cohen class distribution is selected to make a time-frequency analysis of full acoustic wave. In this paper, pore formation with the fluid (oil layer, water layer, oil-water layer) that has different nature and different permeability is analyzed in time-frequency domain, and the characteristics of time-frequency of the full wave propagation in various formations are summarized. Some time-frequency analysis methods in use are compared. Full wave train is made a time-frequency analysis. Permeability, coefficient of viscosity and time-frequency characteristics of the full wave acoustic logging of the formation with different property fluid are summarized. In practice logging, the method of the use of time-frequency distribution characteristics of acoustic waves to identify the formation property is still in the exploratory stage, the time-frequency distribution characteristics of acoustic logging theoretical research has just started.. The research of this paper can enrich the log interpretation method and has some theoretical significance as well as application value.
.To study the effect of formation properties on full wave logging acoustic field, the acoustic field of quasi-elastic medium is calculated. And acoustic field propagation characteristic and the effect of diameter on acoustic field propagation in soft stratum and hard stratum are analyzed. In addition, acoustic field full wave strain in porous media is calculated, too. The effect of various formation parameters on acoustic field in well is obtained by analyzing the two-dimensional spectrum chart. The key to the study is the effect of permeability, coefficient of viscosity and the properties of contained fluid on acoustic wave in well. Several common time-frequency analysis methods are compared. A kind of Choi-Williams distribution of Cohen class distribution is selected to make a time-frequency analysis of full acoustic wave. Porous formations with different propertied fluid and different permeability are made an analysis in time-frequency domain, and the time-frequency characteristics of full wave train logging in various formations are analyzed.
首先,本文根据井中声场理论,数值计算出了准弹性地层中的声场时域波形。利用数值计算出的二维谱分析了在软地层和硬地层两种不同地层中频率-波数域内波场的特征以及井径对声场传播的影响。
其次,为了考察孔隙介质中声场的传播特征,本文以Biot-Rosenbaum声场理论为基础,考虑动态渗透率的影响,引入动态渗透率的近似计算公式,数值计算出了饱和流体孔隙介质中的井孔声场全波列及其二维谱。详细分析了井孔中快纵波、慢纵波以及横波的频散、衰减系数变化等传播特征。
最后,本文利用Choi-Williams时频分析方法,求出了理论时域波形和实测声压波形Choi-Williams时频分布图,对比和分析了不同渗透率和含不同性质流体地层中声波传播的时频特征。
Full wave train in Acoustic Logging is a major breakthrough in the technological development of acoustic logging which makes a regular record of the sliding longitudinal wave (arrival time and amplitude) extended to the records of the sliding longitudinal wave and sliding transverse wave spreading along the wall of borehole and the records of the guided wave in the fluid in the wells between the borehole wall and the instrument’s shell in the pit. There are highly affluent in information about the properties and the characteristics of the wall of the well and stratum and the circumstance of borehole such as various types of wave velocity, amplitude and its attenuation, the change of frequency, the effect of frequency dispersion and the graphics of wave envelope and the like which are included in records. Therefore, in order to obtain these important stratum information, first, the velocity change, amplitude fading, frequency dispersion and otherwise of various partial wave included in full wave train must be considered to make sure that these characteristics have relations with which character of stratum, so we should study the characteristics of wave propagation in stratum with different properties. It is important to study the influence of stratum properties and borehole conditions on the wave propagation. Based on this idea mentioned above, in this paper, the author utilizes a computer to do the numerical calculation of the theory wave profile of wave acoustic logging, and uses the calculated two dimension spectrum combined with time-domain waveform to study and analyze the influence of the change of various stratum parameters to various partial waves in full wave train. In addition, for the sake of extracting more information from full wave train in acoustic logging, the author tries to do some analysis in time-frequency domain. Time-frequency analysis have been done to hole stratum containing fluids with different properties(oil layer, water layer) and the different permeability.
This paper mainly includes three parts. First, the research to the acoustic field propagation properties of elastic medium which includes wave propagation in soft and hard rock stratum and the hole diameter impacting on the acoustic field in the well. Second, the research of the acoustic field in porous media which mainly contains viscosity lag coefficient, permeability and the influence of the fluid properties (oil layer, water layer) make to the acoustic field. Third, the treatments of time-domain waveforms in the acoustic field in the well which mainly includes the comparison of time-frequency analysis methods and time-frequency characteristics of wave propagation in various stratums. The main contents are briefly described below.
In the first place, we see stratum as equivalent elastic formation that is quasi-elastic medium and don’t consider the influence of pore, so that acoustic model can be simplified and the solution of the acoustic field in the borehole can be obtained easily. Without regard to the stratum pore and the fluid contained, acoustic field calculated from quasi-elastic medium model can study and understand the influence which is caused by different properties stratum to the acoustic field better. Based on the theory of the 6 acoustic field in the well in this paper, time-domain waveform of the acoustic field in quasi-elastic stratum was numerical calculation. Two-dimensional spectrum numerical value is applied to analyze the character of two-dimensional spectrum in frequency– wave number domain in the soft stratum and hard stratum and the influence which is caused borehole radius to the acoustic field propagation. Through the two-dimensional spectral of soft stratum in contrast with two-dimensional spectral of hard stratum, and the analysis of character about longitudinal wave (first wave), transverse wave, mud longitudinal wave and phase velocity, group velocity and the change of chroma about two-dimensional amplitude of various model waves, we know that the phase velocity, group velocity of stratum longitudinal wave (first wave), stratum transverse wave, mud longitudinal wave change rarely in borehole acoustic field. Stratum transverse wave and the pseudo-rayleigh wave are not received in borehole axis in soft stratum. Leakage model corresponding to mode waves is a geometric decaying wave. It has the character of fast decay and stronger frequency dispersion in the acoustic field propagation. Transmission modes and characters of waves with the medium which have different properties were studied by two-dimensional amplitude spectrum of acoustic wave calculated in different medium condition.
In the second place, acoustic logging not only offer stratum lithology parameters, such as propagation velocity of longitudinal and transverse wave, but also provide reservoir parameters, such as the porosity, permeability and etc. Reservoir parameters have great significance for gas exploration, because oil gas and etc are stored in reservoir stratum of porous rock. Reservoir stratum is composed of solid phase skeleton. There is a mass of pore spaces which connect each other. Oil gas can store in it and flow oppositely. Mediums with this characteristic are called pore space mediums. Biot theory about the acoustic field propagation in pore space mediums has been widely recognized and applied and is recognized as the best theoretical model of the wave propagation in the description of pore space mediums at present. Pore space medium theory of Biot was applied to the research of acoustic logging by Rosenbaum(1974) for the first time. The influence of reservoir stratum parameters, such as porosity and permeability, on well borehole full acoustic wave information was studied numerically with point source model, and then he found that the permeability and stoneley wave had the closest relation which we called Biot-Roserbaum theory. The concept of the dynamic permeability was advanced by Johnson in 1987 and applied in Biot theory, and an approximate formula of dynamic permeability was given.
In this paper, borehole acoustic field two-dimensional spectrum in saturated fluid porous media was figured out numerically based on Biot-Rosenbaum acoustic wave theory numerical model, the consider of the influence of dynamic permeability and the introduction of approximate computational formula of dynamic permeability. By the use of Biot-Rosenbaum theory numerical model with the consider of the influence of dynamic permeability, fast longitudinal wave, slow longitudinal wave and frequency dispersion curves of transverse wave were calculated, and theoretical acoustic pressure waveform received in a point of well-axis with the given stratum condition was calculated and its two-dimensional spectrum was obtained. Stoneley wave, pseudo-rayleigh wave, longitudinal mode waves, transverse mode waves and the change character of the longitudinal and transverse wave in the condition of different permeability stratum can be seen clearly and directly through the calculated result of borehole acoustic field two-dimensional spectrum and the acoustic pressure waveforms chart in different permeability stratum.
The character of frequency dispersion of fast longitudinal wave, slow longitudinal wave and transverse wave were summarized through calculated frequency dispersion curves based on Biot-Roasenbaum theory numerical model with the consider of with the consider of the influence of dynamic permeability. Fast longitudinal wave and transverse wave has weak frequency dispersion, and the slow longitudinal wave has stronger frequency dispersion. The frequency dispersion of fast longitudinal wave weakened slightly and its speed increased slightly with the increasing of permeability. The frequency dispersion of slow longitudinal wave is strong. it weakened slightly with the increasing of permeability while the speed of the slow longitudinal wave increased evidently. The frequency dispersion of transverse wave weakened while its speed increased faintly with the increasing of permeability.
It can be seen from the calculated two- dimension spectrum that, in the frequency-wave number domain, two-dimensional spectral values has multiple culminating point, each culminating point correspond to the peak value of two-dimensional spectrum, and the peak values of two-dimensional spectrum are distributed in scaly structure in the two-dimensional spectrum. Sundry mode waves correspond to the peak and change with the change of stratum parameters. With the increasing of penetration, the two-dimensional spectrum values and the contribution of pseudo-rayleigh wave decrease relatively, while the contribution of leak mode waves to which longitudinal wave and transverse wave correspond enlarge relatively. As a result, the aggrandizement of permeability makes the losing energy of acoustic field in the geometric attenuation increase. The contribution of pseudo-rayleigh wave and the contribution of leak mode waves which longitudinal wave and transverse wave correspond to decrease relatively. As a result, the aggrandizement of permeability makes the losing energy of acoustic field in the geometric attenuation decrease.
By calculating the acoustic field two-dimensional spectrum and time domain wave column of oil layer and water layer, it can be seen that the contribution of transverse wave and pseudo-rayleigh wave of acoustic wave in oil-bearing formation is bigger than in water bearing ground and the energy of transverse wave and pseudo-rayleigh wave is higher. The contribution of stoneley wave in oil-bearing medium become smaller than water bearing ground, the amplitude and energy of stoneley wave is on the small side.
In this paper, the property of stoneley was studied importantly through two-dimensional spectrum and acoustic pressure waveform chart. It can be seen clearly from acoustic field two-dimensional spectrum in well with the condition of different permeability stratum that the speed of stoneley wave is slightly lower than the speed of the fluid in the well bore. Its frequency dispersion is weak. It has cutoff frequency and the frequency range is lower. Its size is between zero and cutoff frequency. Stoneley wave is sensitive about the change of permeability. The frequency range and amplitude attenuation of stoneley wave were effected by permeability. The amplitude of stoneley attenuates more tempestuously and the cutoff frequency of stoneley are smaller with its frequency range lower when the permeability is bigger. Stoneley wave is sensitive about the change of coefficient of viscosity. The amplitude attenuation of stoneley wave will be smaller and the frequency range of stoneley wave will be bigger while coefficient of viscosity is bigger. Through the study of acoustic field two-dimensional spectrum in the well bore in permeability stratum, we find that stoneley wave is sensitive about the change of permeability and coefficient of viscosity. Its frequency range and amplitude attenuation are influenced by permeability.
Third, in order to extract more information from full wave train in acoustic logging, the author tries to get more information in time-frequency domain. Several used commonly methods of time-frequency analysis are compared. A kind of Choi-Williams distribution of Cohen class distribution is selected to make a time-frequency analysis of full acoustic wave. In this paper, pore formation with the fluid (oil layer, water layer, oil-water layer) that has different nature and different permeability is analyzed in time-frequency domain, and the characteristics of time-frequency of the full wave propagation in various formations are summarized. Some time-frequency analysis methods in use are compared. Full wave train is made a time-frequency analysis. Permeability, coefficient of viscosity and time-frequency characteristics of the full wave acoustic logging of the formation with different property fluid are summarized. In practice logging, the method of the use of time-frequency distribution characteristics of acoustic waves to identify the formation property is still in the exploratory stage, the time-frequency distribution characteristics of acoustic logging theoretical research has just started.. The research of this paper can enrich the log interpretation method and has some theoretical significance as well as application value.
.To study the effect of formation properties on full wave logging acoustic field, the acoustic field of quasi-elastic medium is calculated. And acoustic field propagation characteristic and the effect of diameter on acoustic field propagation in soft stratum and hard stratum are analyzed. In addition, acoustic field full wave strain in porous media is calculated, too. The effect of various formation parameters on acoustic field in well is obtained by analyzing the two-dimensional spectrum chart. The key to the study is the effect of permeability, coefficient of viscosity and the properties of contained fluid on acoustic wave in well. Several common time-frequency analysis methods are compared. A kind of Choi-Williams distribution of Cohen class distribution is selected to make a time-frequency analysis of full acoustic wave. Porous formations with different propertied fluid and different permeability are made an analysis in time-frequency domain, and the time-frequency characteristics of full wave train logging in various formations are analyzed.
引文
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