Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical sol...Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical solution of finite element equations is given.Finally,Properties of elastic wave propagation are observed and analyzed through FEM modeling.展开更多
In this paper we calculate a synthetic medium surface displacement response that is consistent with real measurement data by applying the least-square principle and a niche genetic algorithm to the parameters inversio...In this paper we calculate a synthetic medium surface displacement response that is consistent with real measurement data by applying the least-square principle and a niche genetic algorithm to the parameters inversion problem of the wave equation in a two-phase medium. We propose a niche genetic multi-parameter (including porosity, solid phase density and fluid phase density) joint inversion algorithm based on a two-phase fractured medium in the BISQ model. We take the two-phase fractured medium of the BISQ model in a two- dimensional half space as an example, and carry out the numerical reservoir parameters inversion. Results show that this method is very convenient for solving the parameters inversion problem for the wave equation in a two-phase medium, and has the advantage of strong noise rejection. Relative to conventional genetic algorithms, the niche genetic algorithm based on a sharing function can not only significantly speed up the convergence, but also improve the inversion precision.展开更多
High-frequency seismic attenuation is conventionally attributed to anelastic absorption. In this paper, I present three studies on high-frequency seismic attenuation and propose that the physical mechanism results fro...High-frequency seismic attenuation is conventionally attributed to anelastic absorption. In this paper, I present three studies on high-frequency seismic attenuation and propose that the physical mechanism results from the interference of elastic microscopic multiple scattering waves. First, I propose a new theory on wave propagation in a two-phase medium which is based on the concept that the basic unit for wave propagation is a nano- mass point. As a result of the elasticity variations of pore fluid and rock framework, micro multiple scattering waves would emerge at the wavelength of the seismic waves passing through the two-phase medium and their interference and overlap would generate high- frequency seismic attenuation. Second, I present a study of the frequency response of seismic transmitted waves by modeling thin-layers with thicknesses no larger than pore diameters. Results indicate that high-frequency seismic waves attenuate slightly in a near-surface water zone but decay significantly in a near-surface gas zone. Third, I analyze the seismic attenuation characteristics in near-surface water and gas zones using dual-well shots in the Songliao Basin, and demonstrate that the high-frequency seismic waves attenuate slightly in water zones but in gas zones the 160-1600 Hz propagating waves decay significantly. The seismic attenuation characteristics from field observations coincide with the modeling results. Conclusions drawn from these studies theoretically support seismic attenuation recovery.展开更多
The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and ...The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and attenuation of elastic waves in the porous medium are widely investigated in recent years. However, we have not read any reports on numerical simulation based on the BISQ equation. In this paper, following the BISQ equation, elastic wave propagation in the transversely isotropic porous medium filled with fluids is simulated by the stag-gered grid method for different frequency and phase boundary cases and the two-layer medium. And propagating characteristics of seismic and acoustic waves and various phenomena occured in the propagating process are in-vestigated when the two mechanisms are considered simultaneously.展开更多
To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of ...To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.展开更多
We give a sufficient condition for uniqueness for the pressure/saturation system. We establish this condition through analytic arguments, and then construct 'mobilities' (or mobility-like functions) that satis...We give a sufficient condition for uniqueness for the pressure/saturation system. We establish this condition through analytic arguments, and then construct 'mobilities' (or mobility-like functions) that satisfy the new condition (when the parameter is 2). For the constructed 'mobilities', we do graphical experiments that show, empirically, that this condition could be satisfied for other values of . These empirical experiments indicate that the usual smoothness condition on the fractional flow function (and on the total mobility), for uniqueness and convergence, might not be necessary. This condition is also sufficient for the convergence of a family of perturbed problems to the original pressure/saturation problem.展开更多
To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order vel...To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic (VTI) media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.展开更多
We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot's equations and Johnson's bulk modulus. We solve the equations, obtain the attenuat...We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot's equations and Johnson's bulk modulus. We solve the equations, obtain the attenuation coefficients, and analyze the characteristics of wave attenuation in the seismic frequency range. The results suggest that seismic waves show attenuation and dispersion in partially saturated rocks in the low frequency range. With frequency increasing, attenuation increases. The attenuation of P-waves of the second kind is more pronounced in agreement with Biot's theory. We also study the effect of porosity, saturation, and inner sphere radius on the attenuation of the P-waves of the first kind and find that attenuation increases with increasing frequency and porosity, and decreases with increasing frequency and degree of saturation. As for the inner sphere radius, wave attenuation is initially increasing with increasing frequency and inner sphere radius less than half the outer radius. Subsequently, wave attenuation decreases with increasing frequency and inner sphere radius is higher than half the outer sphere radius.展开更多
Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a genera...Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green's second identity. This theory can be reduced to a number of the most typical mild-slope equations currently in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.展开更多
When gas invasion,especially overflow,occurs at the bottom hole in the process of managed pressure drilling(MPD),it is common to apply backpressure on the wellbore by adjusting the backpressure pump and throttle valve...When gas invasion,especially overflow,occurs at the bottom hole in the process of managed pressure drilling(MPD),it is common to apply backpressure on the wellbore by adjusting the backpressure pump and throttle valve,so as to rebuild bottom hole pressure balance.If it is still thought that the wellhead backpressure is loaded to the bottom hole instantaneously,there will be larger errors between the calculated wellbore parameters and the actual wellbore flow parameters,which will result in well control failure and even well blowout.In this paper,a pressure wave propagation equation suitable for the gaseliquid two-phase flow in the annulus was established based on the global averaged gaseliquid two-phase flow model to investigate the propagation velocity and time of backpressure wave in the wellbore.Then,gaseliquid interaction was introduced to carry out coupling solution on the equation set.It is shown that pressure wave velocity increases with the increase of drilling mud density,but decreases with the increase of void fraction and virtual mass force coefficient.It changes drastically at first,and then slows down.What's more,when the void fraction is greater than 0.1 or the virtual mass force coefficient exceeds 0.2,the momentum between gas phase and liquid phase is fully exchanged,and the pressure wave velocity decreases slowly,approaching a stable value.In Well Penglai 9 in the Sichuan Basin,for example,the average time of single pressure wave propagation is about 50 s,and the total propagation time of 4 rounds is about 200 s,which accounts for more than 67%of the total time of system control response.It is indicated that the propagation velocity and time of the pressure wave in the annulus calculated by this method can greatly improve the accuracy of managed pressure response time of MPD drilling system and the control precision of adaptive throttle valve.展开更多
Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational ax-isymmetric dusty gas, which has a variable azimuthal and axia...Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational ax-isymmetric dusty gas, which has a variable azimuthal and axial fluid velocity. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The equi-librium flow conditions are assumed to be maintained, and the density of the mixture is assumed to be varying and obeying an exponential law. The fluid velocities in the ambient medium are assumed to obey exponential laws. The shock wave moves with variable velocity. The effects of variation of the mass concentration of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times. Also, a comparison between the solutions in the cases of isothermal and adia-batic flows is made.展开更多
In this work, we present the study of electromagnetic wave propagation through a medium with a variable dielectric function using the concept of Gaussian Beam. First of all, we start with wave equation with which we o...In this work, we present the study of electromagnetic wave propagation through a medium with a variable dielectric function using the concept of Gaussian Beam. First of all, we start with wave equation with which we obtain the solution in terms of the electric field and intensity distributions approximate to Gaussian Function, . With this, we analyze the dependency of r on Gaussian beam distribution spread, the distant from the axis at which the intensity of the beam distribution begins to fall at a given estimate of its peak value. The influence of the optimum beam waist wo and the beam spread on the intensity distribution will also be analyzed.展开更多
波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风...波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。展开更多
A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and ...A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and Hankel transform. However, the method may not always be valid. The work is extended to the general case being in the rectangular coordinate. The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface. Based on Biot's theory for fluid- saturated porous media, the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions. Then, using the technique of double Fourier transform, the governing differential equations were easily solved. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained. Furthermore, a systematic study on half-space problem in saturated soils was performed. Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone, considering both case of drained surface and undrained surface, were presented.展开更多
摘要Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical solution of finite element equations is given.Finally,Properties of elastic wave propagation are observed and analyzed through FEM modeling.
基金sponsored by the National Science and Technology Major Project(Grant No.2011ZX05025-001-07)
摘要In this paper we calculate a synthetic medium surface displacement response that is consistent with real measurement data by applying the least-square principle and a niche genetic algorithm to the parameters inversion problem of the wave equation in a two-phase medium. We propose a niche genetic multi-parameter (including porosity, solid phase density and fluid phase density) joint inversion algorithm based on a two-phase fractured medium in the BISQ model. We take the two-phase fractured medium of the BISQ model in a two- dimensional half space as an example, and carry out the numerical reservoir parameters inversion. Results show that this method is very convenient for solving the parameters inversion problem for the wave equation in a two-phase medium, and has the advantage of strong noise rejection. Relative to conventional genetic algorithms, the niche genetic algorithm based on a sharing function can not only significantly speed up the convergence, but also improve the inversion precision.
摘要High-frequency seismic attenuation is conventionally attributed to anelastic absorption. In this paper, I present three studies on high-frequency seismic attenuation and propose that the physical mechanism results from the interference of elastic microscopic multiple scattering waves. First, I propose a new theory on wave propagation in a two-phase medium which is based on the concept that the basic unit for wave propagation is a nano- mass point. As a result of the elasticity variations of pore fluid and rock framework, micro multiple scattering waves would emerge at the wavelength of the seismic waves passing through the two-phase medium and their interference and overlap would generate high- frequency seismic attenuation. Second, I present a study of the frequency response of seismic transmitted waves by modeling thin-layers with thicknesses no larger than pore diameters. Results indicate that high-frequency seismic waves attenuate slightly in a near-surface water zone but decay significantly in a near-surface gas zone. Third, I analyze the seismic attenuation characteristics in near-surface water and gas zones using dual-well shots in the Songliao Basin, and demonstrate that the high-frequency seismic waves attenuate slightly in water zones but in gas zones the 160-1600 Hz propagating waves decay significantly. The seismic attenuation characteristics from field observations coincide with the modeling results. Conclusions drawn from these studies theoretically support seismic attenuation recovery.
基金State Natural Sciences Foundation of China (No. 40174012) and the Key Laboratory Foundation of the CNPC (No. GPKL0104).
摘要The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and attenuation of elastic waves in the porous medium are widely investigated in recent years. However, we have not read any reports on numerical simulation based on the BISQ equation. In this paper, following the BISQ equation, elastic wave propagation in the transversely isotropic porous medium filled with fluids is simulated by the stag-gered grid method for different frequency and phase boundary cases and the two-layer medium. And propagating characteristics of seismic and acoustic waves and various phenomena occured in the propagating process are in-vestigated when the two mechanisms are considered simultaneously.
摘要To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.
摘要We give a sufficient condition for uniqueness for the pressure/saturation system. We establish this condition through analytic arguments, and then construct 'mobilities' (or mobility-like functions) that satisfy the new condition (when the parameter is 2). For the constructed 'mobilities', we do graphical experiments that show, empirically, that this condition could be satisfied for other values of . These empirical experiments indicate that the usual smoothness condition on the fractional flow function (and on the total mobility), for uniqueness and convergence, might not be necessary. This condition is also sufficient for the convergence of a family of perturbed problems to the original pressure/saturation problem.
基金supported by the National High-Tech Research and Development Program of China(Grant No.2006AA06Z202)the Open Fund of the Key Laboratory of Geophysical Exploration of CNPC(Grant No.GPKL0802)+1 种基金the Graduate Student Innovation Fund of China University of Petroleum(East China)(Grant No.S2008-1)the Program for New Century Excellent Talents in University(Grant No.NCET-07-0845)
摘要To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic (VTI) media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.
基金supported by the National Natural Science Foundation of China(Nos.41204089 and 41174087)the National Science and Technology Major Project(Nos.2011ZX05035-001 and 2011ZX05005-005)the National 863 Program(No.2013AA064201)
摘要We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot's equations and Johnson's bulk modulus. We solve the equations, obtain the attenuation coefficients, and analyze the characteristics of wave attenuation in the seismic frequency range. The results suggest that seismic waves show attenuation and dispersion in partially saturated rocks in the low frequency range. With frequency increasing, attenuation increases. The attenuation of P-waves of the second kind is more pronounced in agreement with Biot's theory. We also study the effect of porosity, saturation, and inner sphere radius on the attenuation of the P-waves of the first kind and find that attenuation increases with increasing frequency and porosity, and decreases with increasing frequency and degree of saturation. As for the inner sphere radius, wave attenuation is initially increasing with increasing frequency and inner sphere radius less than half the outer radius. Subsequently, wave attenuation decreases with increasing frequency and inner sphere radius is higher than half the outer sphere radius.
摘要Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green's second identity. This theory can be reduced to a number of the most typical mild-slope equations currently in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.
基金Project supported by General Program of National Natural Science Foundation of China“Wellbore Multi-phase Flow Coupling Mechanism Research-Formations Based on Precise Backpressure Control”(No.:51474073)“Research on Wellbore Temperature Field and Pressure Field Distribution Laws of Deep Unbalanced Drilling Based on Thermal-fluid Coupling”(No.:51374077).
摘要When gas invasion,especially overflow,occurs at the bottom hole in the process of managed pressure drilling(MPD),it is common to apply backpressure on the wellbore by adjusting the backpressure pump and throttle valve,so as to rebuild bottom hole pressure balance.If it is still thought that the wellhead backpressure is loaded to the bottom hole instantaneously,there will be larger errors between the calculated wellbore parameters and the actual wellbore flow parameters,which will result in well control failure and even well blowout.In this paper,a pressure wave propagation equation suitable for the gaseliquid two-phase flow in the annulus was established based on the global averaged gaseliquid two-phase flow model to investigate the propagation velocity and time of backpressure wave in the wellbore.Then,gaseliquid interaction was introduced to carry out coupling solution on the equation set.It is shown that pressure wave velocity increases with the increase of drilling mud density,but decreases with the increase of void fraction and virtual mass force coefficient.It changes drastically at first,and then slows down.What's more,when the void fraction is greater than 0.1 or the virtual mass force coefficient exceeds 0.2,the momentum between gas phase and liquid phase is fully exchanged,and the pressure wave velocity decreases slowly,approaching a stable value.In Well Penglai 9 in the Sichuan Basin,for example,the average time of single pressure wave propagation is about 50 s,and the total propagation time of 4 rounds is about 200 s,which accounts for more than 67%of the total time of system control response.It is indicated that the propagation velocity and time of the pressure wave in the annulus calculated by this method can greatly improve the accuracy of managed pressure response time of MPD drilling system and the control precision of adaptive throttle valve.
摘要Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational ax-isymmetric dusty gas, which has a variable azimuthal and axial fluid velocity. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The equi-librium flow conditions are assumed to be maintained, and the density of the mixture is assumed to be varying and obeying an exponential law. The fluid velocities in the ambient medium are assumed to obey exponential laws. The shock wave moves with variable velocity. The effects of variation of the mass concentration of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times. Also, a comparison between the solutions in the cases of isothermal and adia-batic flows is made.
摘要In this work, we present the study of electromagnetic wave propagation through a medium with a variable dielectric function using the concept of Gaussian Beam. First of all, we start with wave equation with which we obtain the solution in terms of the electric field and intensity distributions approximate to Gaussian Function, . With this, we analyze the dependency of r on Gaussian beam distribution spread, the distant from the axis at which the intensity of the beam distribution begins to fall at a given estimate of its peak value. The influence of the optimum beam waist wo and the beam spread on the intensity distribution will also be analyzed.
摘要波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。
摘要A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and Hankel transform. However, the method may not always be valid. The work is extended to the general case being in the rectangular coordinate. The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface. Based on Biot's theory for fluid- saturated porous media, the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions. Then, using the technique of double Fourier transform, the governing differential equations were easily solved. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained. Furthermore, a systematic study on half-space problem in saturated soils was performed. Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone, considering both case of drained surface and undrained surface, were presented.