摘要
对于由弹性波场激发所引起的电磁场变化效应震电效应的研究,正成为勘探地球物理领域,特别是油气勘探开发业界的关注热点。震电效应应用于油气勘探开发,特别是在寻找剩余油方面前景十分诱人,其产生的电磁波场对地下油气藏分布也具有直接探测性。由此,本文旨在研究震电效应下,平面声波在流体与孔隙介质分界面上的折反射,围绕这个主题开展了研究。
本文对研究震电所需的理论基础——Biot理论进行了简单介绍,Biot建立了流体饱和孔隙介质弹性波动力学理论,该理论对研究的孔隙介质作了一些假设后,得到了应力应变关系和运动方程,给出了均匀孔隙介质中的平面波解,并且对孔隙介质中是否存在慢纵波进行了预测。
本文简单介绍了震电效应产生的机理,弹性波在孔隙介质中传播时,填充在孔隙中的流体会相对于固相骨架运动,形成波动渗流。若孔隙中的流体含净剩电荷,这种波动渗流则会引起电磁场。相反,电磁场可引起渗流和固相骨架运动,形成弹性波。这种叫做动电耦合现象,在地震频率范围称为震电效应。
Pride建立了声场和电磁场的耦合方程组,本文通过对电场矢量和位移矢量进行亥姆霍兹分解,把用电场矢量和位移矢量表示的Pride声电耦合方程组转化为关于势函数的波动方程组,在平面直角坐标中导出在流体饱和空隙介质中声电耦合场的形式解,通过声电耦合问题的边界条件,独立编制了计算程序,计算了能流折反射系数,计算表明边界上法向能流连续,证明程序的正确性。通过数值模拟,可以获得折反射系数随不同入射角和不同频率的变化规律,计算结果表明电磁波能量反射和透射系数都是在某一频率值达到最大后,随频率的增大而逐渐减小;流体与孔隙介质界面不同的边界状况对能量折反射系数也有明显的影响。折反射系数不仅与入射角度和频率有关,也和地层的其他参数有关,本文模型和编制的程序为进一步详细深入研究它们的关系提供理论基础和计算软件。
此外,为了提高计算效率,我们先独立求解了声场,分别采用非耦合和似稳法进行研究。非耦合法则是在忽略声波诱导电磁场对声场影响的前提下,将Pride声电耦合方程组简化为求解具有波动电流源的麦克斯韦方程组;然后引入赫兹矢量,把求解具有波动电流源的麦克斯韦方程组问题转化为求解关于赫兹矢量的非齐次矢量亥姆霍兹方程组;运用标量亥姆霍兹方程的解,找出非齐次矢量亥姆霍兹方程组的一组特解,与齐次亥姆霍兹方程组的通解叠加,得出电场、磁场的表达式,由于非耦合法计算上也相对复杂,本文只对其进行了理论研究。似稳法同样是忽略声波诱导电磁场对声场影响的前提下,把低频电磁场看成似稳场,引入电势后,利用了边界条件求出电场,再利用电场进一步确定电流密度和磁场强度。通过独立编程初步试算表明,简化的算法编制的程序相对简单,在低于1千赫兹频率以下与严格解求得的电场反射系数比相对误差在10-5,说明在地震频率范围内完全可以采用似稳法提高计算效率。
本文的研究结果表明:平面分层介质声电耦合波折反射系数是与入射角度、频率及地层参数有关的;采用完成的Pride动电耦合方程得到的折反射系数公式体系和编制的程序为其它简化方法提供严格比较标准;似稳法简单而且计算效率高在地震和测井频率范围值得采用。本文的理论研究结果、编制的程序对水平夹层介质中声电耦合波的特性等其他声电耦合波场的课题提供了参考价值。
The research on seismoelectric effect which is the changing effect of the electromagnetic field which is caused by elastic wave field is becoming the hot concerned by exploration geophysics, especially oil and gas exploration and development of the industry. This paper is aimed to study Reflection and transmission of the plane wave at a fluid/fluid-saturated poroelastic solid interface with seismoelectric effect.So we launch the following research around this one theme.
Biot established the mechanics theory of elastic wave in fluid-saturated porous media, which to be called Biot’s theory. This theory made some assumptions to the porous media to be research: (1)the scale of pore and solid-phase particle is far less than the wavelength; (2)the pore is connected; (3) Solid-phase are connected. In these assumptions, Biot obtained the stress-strain relations and equations of motion, and gived the plane wave’s solutions in the uniform pore medium The theory forecasted whether exist slow P wave in porous media.
This article simply introduces the production mechanism of seismoelectric effect. The elastic waves are coupled with the electromagnetic waves if there is an electric double layer (EDL) at the mineral-water interface. It is explained why such a coupling occurs when a fast P wave or a slow P waves, or a shear wave propagates. It is noted that electrokinetic effect is related to fluid motion, and is primarily related to ion migration in the movable fluid.
Pride established the coupling equations of sound field and electromagnetic. To solve the Pride's governing equations, the Helmholtz potential functions are used to express the frame and fluid displacement vectors and the electric field vector,transforming the governing equations into wave equations about the potential functions. Under rectangular coordinate system the formal solution of the coupling field in fluid-saturated porous media is derived. Through the boundary conditions of the coupling problem, the reflection and transmission coefficient of energy fluxes are calculated in theory. By numerical simulation, we learned that changing incident angle and frequency can obtain the coefficients which are needed, and after achieving maximum at a frequency value the reflection and transmission coefficients of electromagnetic energy are gradually decrease as the frequency increasing. In different boundary conditions, there are some differences on the energy reflection coefficients.The reflection and transmission coefficient is not only related with the incident angle and frequency, but also related with the other parameters, This model and procedures provided a theoretical basis for further detailed in-depth study of their relationship.
If sound field is solved independently, the reflection and transmission problem can be studied by non-coupling method and the seemingly stable law. Non-coupling rule is that ignoring electromagnetic fields induced by acoustic effecting on the sound field, and make the Pride coupled equations reduce to solving the Maxwell's equations with fluctuations in the current source; Then cited Hertz vector, the problem solving the Maxwell's equations with fluctuations in the current source is transformed into solving the problem on the Hertz vector of the non-homogeneous vector Helmholtz equation; Using the solutionof scalar Helmholtz equation, to find a special solution of non-homogeneous vector Helmholtz equations and then superposition with general solution of homogeneous Helmholtz equation, drawing the expression of electric and magnetic fields, getting the accuracy of this method through simulation results. The seemingly stable method is also ignoring electromagnetic fields induced by acoustic effecting on the sound field, making the low-frequency electromagnetic fields as seemingly stable field, after the introduction of electric potential, using the boundary conditions to solve electric field, and then using electric fields to further define the current density and magnetic field strength, and similarly, used FORTRAN software simulation, the method also seems to be accuracy.
The numerical simulations in this paper show that plane layered media twists and turns the sound reflection coefficient of coupling with the incident angle, frequency, and the formation parameters, to further clarify the sense of sound field coupling with electromagnetic, it is necessary to carry out the following research projects: characteristic of sound field coupling with electromagnetic wave in level mezzanine media; acoustic-electric well logging and simulation; rock parameters effect on the Electrokinetic coupling coefficient.
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