非均匀复杂地层随钻电磁波测井响应研究
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摘要
随着石油工业的不断发展以及开发油藏地质情况的日益复杂,新的测井方法不断涌现,其中发展最迅猛的是随钻测井技术。新的测井环境和测井方法为测井研究者带来了新的挑战,如新式随钻电磁波测井仪器的性能评价,大斜度井、水平井中随钻电磁波仪器的响应特征,常规普通感应与随钻电磁波仪器探测性能的区别等。通过数值模拟可以为这些问题的解决提供一种有效的途径。本论文的目的就是通过对一维、二维以及全三维地层模型数值模拟方法的研究,为实际问题的解决提供可行的方法平台。
本论文第二章,第三章介绍径向分层模型以及层状介质地层模型电磁场分布的公式推导以及高效计算方法,将感应测井仪器发射源简化为一系列的磁偶极子,其在层状地层中产生的电磁场分解成彼此独立的横电波(TE)和横磁波(TM),得到层状地层电磁场含有Bessel函数的解析解。在充分分析被积函数特点的前提下,采用改进的高斯方法直接计算Bessel函数的无穷域积分代替传统的傅立叶—汉克尔变换方法。该数值模拟方法对于快速分析层厚、井斜等地层因素对电磁波测井响应的影响具有很好的效果。
第四章介绍目前应用最广泛的二维问题计算方法,主要介绍了逐次逼近法和模式匹配方法,其中逐次逼近方法的思想对感应测井的反演有重要意义。模式匹配法采用张庚骥先生构造的幅度基函数和斜度基函数,这保证了电磁场本身及其一阶导数连续,因此只需少量基函数就能得到较高的精度。数值模拟表明,只要选择适当的网格划分方法以及适量的基函数,模式匹配法对中低频的普通感应以及高频的随钻电磁波测井响应模拟都有很好的效果,而且是目前常用的数值模拟方法中计算效率最高的一种方法。
第五章介绍随钻电磁波三维频率域数值模拟方法。本章从Maxwell电磁响应方程出发,针对大斜度井井眼和侵入剖面的几何特点,采用新的网格划分方法,并应用基于交错网格的有限差分得到了三维频率域电磁响应差分计算格式,利用电场的镜像对称性,使计算规模减小一半。采用改进的ICCG(不完全乔尔斯基共轭梯度)方法,对一维变带宽存储的大型复稀疏矩阵进行了求解,得到了随钻电磁波测井响应。通过与解析解的对比表明:该方法能较好的解决电磁场的三维计算问题,但对于各向异性地层模型背景电导率的取值原则仍需进一步研究。
第六章在前面数值模拟方法的研究基础上,以EWR—Phase4仪器为例,着重研究随钻电磁波测井响应的各种影响因素,包括随钻电磁波仪器工作频率的选择、仪器的探测性能、围岩与层厚、井眼、泥浆侵入、井斜、介电常数以及地层各向异性的影响等,对仪器的研发制造以及测井资料的解释评价提供很好的理论依据。
第七章提出了一种新的随钻补偿仪器研发思路。由于随钻电磁波仪器自身的特点,井眼垮塌对仪器响应影响很大,尤其是在盐水泥浆条件下,因此对测井资料进行补偿非常必要,传统的补偿方法使仪器长度增大了近一倍。本章在基于电磁场互换原理的基础上,提出了一种新的仪器补偿方法,可以减小同样探测性能仪器的长度。
With the rapid progress of the oil industry and the increasingly complicated geologic status of reservoir, many new logging methods come forth continuously. Logging while drilling method is one of the most rapidly developing method. New logging environments and methods bring new challenges to the logging researchers, such as new electromagnetic LWD instruments capability, the response of electromagnetic LWD instruments in highly deviated or horizontal wells, the different detection ability between the traditional induction logging tools and electromagnetic LWD instruments. Numerical simulation can serve as an efficient tool to solve these problems. The objective of this dissertation is to attempt to provide a feasible methodological platform by the study of numerical simulation in 1D, 2D and 3D formation models.
In chapter 2 and 3, the electromagnetic distribution formulate of radially layered and stratified formation is introduced with high efficient algorithm. The transmitting coils of induction logging instruments are simplified as series of magnetic dipoles, electromagnetic wave is resolved as TE and TM wave in horizontal layers, and the analysis results which include integration of Bessel function are obtained in the dissertation. Improved Gauss numerical integral method is used to calculate the infinite integration of Bessel function instead of traditional Fourier-Henkel transform method. The numerical simulation method is effective to analysis the effect of the shoulder and the borehole deviation on the response of LWD electrical instruments.
The widely used 2D algorithm is introduced in chapter 4. Successive method and numerical model matching method are addressed. The successive method is meaningful to the inversion of induction logging data. Amplitude basis function and slope basis function built by Mr. Zhang Geng-ji are used in the method of NMM. New basis function guarantee the continuity of the field itself and its first-order derivation, so only a small quantity of basis function are needed to get a high accuracy. The simulation results show that NMM is the most effective algorithm to simulate the response of low frequency induction logging and high frequency electromagnetic LWD instruments by choosing proper mesh and proper amount of basis functions.
In chapter 5 a 3D algorithm for electromagnetic LWD simulation in frequency domain is introduced. The difference equations to calculate the electromagnetic response are deserved from Maxwell’s equations by using staged-grid finite difference method. A new mesh generation method is adopted according to the geometric characteristics of deviated well models with borehole and invasion. The mirror symmetry of the electric field is involved to largely reduce the computation scale. The large scale complex equations are stored by one-dimensional variant-banded and are solved by the method of improved incomplete Choleskey conjugate gradient and the response of electromagnetic LWD tool is deserved. The simulation results show that the algorithm can solve the 3D problem effectively by contrast with analytical results, but the adoption principle of background conductivity should be further studied.
Taking EWR-Phase4 as an example, various influence factors are studied on the basis of several numerical simulation methods in chapter 6. The research contents include that the choosing of work frequency, the investigation ability, the influence of shoulder and thickness, borehole, mud-filtrate invasion, deviation of borehole, dielectric constant and anisotropy. The study can provide theoretical basis for the instrument manufacture and logging data interpretation.
A new research idea of compensated tools is proposed in chapter 7. Borehole slump has great influence on the response of electromagnetic tools because of the characteristics of the tools, especially when the mud is salty. It is necessary to compensate the logging data. Traditional compensation method makes the tool one time longer. A new compensation method is proposed which can reduce the length of tools greatly on the basis of reciprocity principle of electromagnetic.
本论文第二章,第三章介绍径向分层模型以及层状介质地层模型电磁场分布的公式推导以及高效计算方法,将感应测井仪器发射源简化为一系列的磁偶极子,其在层状地层中产生的电磁场分解成彼此独立的横电波(TE)和横磁波(TM),得到层状地层电磁场含有Bessel函数的解析解。在充分分析被积函数特点的前提下,采用改进的高斯方法直接计算Bessel函数的无穷域积分代替传统的傅立叶—汉克尔变换方法。该数值模拟方法对于快速分析层厚、井斜等地层因素对电磁波测井响应的影响具有很好的效果。
第四章介绍目前应用最广泛的二维问题计算方法,主要介绍了逐次逼近法和模式匹配方法,其中逐次逼近方法的思想对感应测井的反演有重要意义。模式匹配法采用张庚骥先生构造的幅度基函数和斜度基函数,这保证了电磁场本身及其一阶导数连续,因此只需少量基函数就能得到较高的精度。数值模拟表明,只要选择适当的网格划分方法以及适量的基函数,模式匹配法对中低频的普通感应以及高频的随钻电磁波测井响应模拟都有很好的效果,而且是目前常用的数值模拟方法中计算效率最高的一种方法。
第五章介绍随钻电磁波三维频率域数值模拟方法。本章从Maxwell电磁响应方程出发,针对大斜度井井眼和侵入剖面的几何特点,采用新的网格划分方法,并应用基于交错网格的有限差分得到了三维频率域电磁响应差分计算格式,利用电场的镜像对称性,使计算规模减小一半。采用改进的ICCG(不完全乔尔斯基共轭梯度)方法,对一维变带宽存储的大型复稀疏矩阵进行了求解,得到了随钻电磁波测井响应。通过与解析解的对比表明:该方法能较好的解决电磁场的三维计算问题,但对于各向异性地层模型背景电导率的取值原则仍需进一步研究。
第六章在前面数值模拟方法的研究基础上,以EWR—Phase4仪器为例,着重研究随钻电磁波测井响应的各种影响因素,包括随钻电磁波仪器工作频率的选择、仪器的探测性能、围岩与层厚、井眼、泥浆侵入、井斜、介电常数以及地层各向异性的影响等,对仪器的研发制造以及测井资料的解释评价提供很好的理论依据。
第七章提出了一种新的随钻补偿仪器研发思路。由于随钻电磁波仪器自身的特点,井眼垮塌对仪器响应影响很大,尤其是在盐水泥浆条件下,因此对测井资料进行补偿非常必要,传统的补偿方法使仪器长度增大了近一倍。本章在基于电磁场互换原理的基础上,提出了一种新的仪器补偿方法,可以减小同样探测性能仪器的长度。
With the rapid progress of the oil industry and the increasingly complicated geologic status of reservoir, many new logging methods come forth continuously. Logging while drilling method is one of the most rapidly developing method. New logging environments and methods bring new challenges to the logging researchers, such as new electromagnetic LWD instruments capability, the response of electromagnetic LWD instruments in highly deviated or horizontal wells, the different detection ability between the traditional induction logging tools and electromagnetic LWD instruments. Numerical simulation can serve as an efficient tool to solve these problems. The objective of this dissertation is to attempt to provide a feasible methodological platform by the study of numerical simulation in 1D, 2D and 3D formation models.
In chapter 2 and 3, the electromagnetic distribution formulate of radially layered and stratified formation is introduced with high efficient algorithm. The transmitting coils of induction logging instruments are simplified as series of magnetic dipoles, electromagnetic wave is resolved as TE and TM wave in horizontal layers, and the analysis results which include integration of Bessel function are obtained in the dissertation. Improved Gauss numerical integral method is used to calculate the infinite integration of Bessel function instead of traditional Fourier-Henkel transform method. The numerical simulation method is effective to analysis the effect of the shoulder and the borehole deviation on the response of LWD electrical instruments.
The widely used 2D algorithm is introduced in chapter 4. Successive method and numerical model matching method are addressed. The successive method is meaningful to the inversion of induction logging data. Amplitude basis function and slope basis function built by Mr. Zhang Geng-ji are used in the method of NMM. New basis function guarantee the continuity of the field itself and its first-order derivation, so only a small quantity of basis function are needed to get a high accuracy. The simulation results show that NMM is the most effective algorithm to simulate the response of low frequency induction logging and high frequency electromagnetic LWD instruments by choosing proper mesh and proper amount of basis functions.
In chapter 5 a 3D algorithm for electromagnetic LWD simulation in frequency domain is introduced. The difference equations to calculate the electromagnetic response are deserved from Maxwell’s equations by using staged-grid finite difference method. A new mesh generation method is adopted according to the geometric characteristics of deviated well models with borehole and invasion. The mirror symmetry of the electric field is involved to largely reduce the computation scale. The large scale complex equations are stored by one-dimensional variant-banded and are solved by the method of improved incomplete Choleskey conjugate gradient and the response of electromagnetic LWD tool is deserved. The simulation results show that the algorithm can solve the 3D problem effectively by contrast with analytical results, but the adoption principle of background conductivity should be further studied.
Taking EWR-Phase4 as an example, various influence factors are studied on the basis of several numerical simulation methods in chapter 6. The research contents include that the choosing of work frequency, the investigation ability, the influence of shoulder and thickness, borehole, mud-filtrate invasion, deviation of borehole, dielectric constant and anisotropy. The study can provide theoretical basis for the instrument manufacture and logging data interpretation.
A new research idea of compensated tools is proposed in chapter 7. Borehole slump has great influence on the response of electromagnetic tools because of the characteristics of the tools, especially when the mud is salty. It is necessary to compensate the logging data. Traditional compensation method makes the tool one time longer. A new compensation method is proposed which can reduce the length of tools greatly on the basis of reciprocity principle of electromagnetic.
引文
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