石油地球物理勘探中若干反问题研究
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摘要
本文研究了石油地球物理勘探中若干反演问题,其中包括自然电位(SP)测井中电阻率识别,核磁共振(NMR)多指数反演,双频电磁波电导率成像,油藏边界识别等。具体安排如下:
第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型,证明了该边值问题弱解的存在唯一性,在此基础上研究了自然电位测井电阻率识别问题:然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法,利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响,取得了满意的结果。
第二章改进了近年发展起来的差分进化(DE)算法,研究核磁共振T_2谱多指数反演问题。从计算精度、抗噪能力和计算速度上来说,取得了满意的结果,较传统算法有一定的优势。
第三章利用一些求病态线性方程组的成熟算法,如截断奇异值分解(TSVD)、最小二乘QR(LSQR)分解、Tikhonov正则化和联合代数重建算法(SART)等方法,研究双频电磁波电导率成像反问题。提出了一种基于LSQR的混合差分进化算法(HDE),研究地球物理线性反演问题。
第四章借鉴逆热传导问题估计边界上热流量的方法,提出了一种基于共轭梯度(CG)算法的反演方法,识别任意给定油藏区域边界上的水侵量。
In this Ph.D.thesis,the author considers some inverse problems including identification of resistance in SP log,multi-exponential inversion of T_2 spectrum in Nuclear Magnetic Resonance(NMR),conductivity imaging using dual-frequency EM Data,identification of boundary water fluxes of oil reservoir and so on,which arise in oil geophysical prospecting.The thesis is organized as follows:
In Chapter 1,a new partial differential equation model for Spontaneous Potential (SP) log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.
In Chapter 2,we improve the Differential Evolution(DE) algorithm developed rapidly in recent years,and apply it to study the multi-exponential inversion problem in nuclear magnetic resonance.Satisfactory results are obtained,and the new algorithm has more advantages in speed,accuracy and anti-noise capability than conventional ones.
In Chapter 3,we study the conductivity imaging using dual-frequency EM Data by some existing algorithms for ill-conditioned linear systems,such as Truncated Singular Value Decomposition(TSVD),Tikhonov regularization,Least Squares QR(LSQR) decomposition and Simultaneous Algebraic Reconstruction Technique (SART).Then a new Hybrid Differential Evolution(HDE) algorithm based on LSQR is proposed to solve linear inverse problems in geophysics.
In Chapter 4,follow the approach to solve inverse heat conduction problem of estimating the unknown boundary heat fluxes,we propose an inversion algorithm based on Conjugate Gradient(CG) method to automatically identify boundary water fluxes in fixed oil reservoir with arbitrary geometry.
第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型,证明了该边值问题弱解的存在唯一性,在此基础上研究了自然电位测井电阻率识别问题:然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法,利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响,取得了满意的结果。
第二章改进了近年发展起来的差分进化(DE)算法,研究核磁共振T_2谱多指数反演问题。从计算精度、抗噪能力和计算速度上来说,取得了满意的结果,较传统算法有一定的优势。
第三章利用一些求病态线性方程组的成熟算法,如截断奇异值分解(TSVD)、最小二乘QR(LSQR)分解、Tikhonov正则化和联合代数重建算法(SART)等方法,研究双频电磁波电导率成像反问题。提出了一种基于LSQR的混合差分进化算法(HDE),研究地球物理线性反演问题。
第四章借鉴逆热传导问题估计边界上热流量的方法,提出了一种基于共轭梯度(CG)算法的反演方法,识别任意给定油藏区域边界上的水侵量。
In this Ph.D.thesis,the author considers some inverse problems including identification of resistance in SP log,multi-exponential inversion of T_2 spectrum in Nuclear Magnetic Resonance(NMR),conductivity imaging using dual-frequency EM Data,identification of boundary water fluxes of oil reservoir and so on,which arise in oil geophysical prospecting.The thesis is organized as follows:
In Chapter 1,a new partial differential equation model for Spontaneous Potential (SP) log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.
In Chapter 2,we improve the Differential Evolution(DE) algorithm developed rapidly in recent years,and apply it to study the multi-exponential inversion problem in nuclear magnetic resonance.Satisfactory results are obtained,and the new algorithm has more advantages in speed,accuracy and anti-noise capability than conventional ones.
In Chapter 3,we study the conductivity imaging using dual-frequency EM Data by some existing algorithms for ill-conditioned linear systems,such as Truncated Singular Value Decomposition(TSVD),Tikhonov regularization,Least Squares QR(LSQR) decomposition and Simultaneous Algebraic Reconstruction Technique (SART).Then a new Hybrid Differential Evolution(HDE) algorithm based on LSQR is proposed to solve linear inverse problems in geophysics.
In Chapter 4,follow the approach to solve inverse heat conduction problem of estimating the unknown boundary heat fluxes,we propose an inversion algorithm based on Conjugate Gradient(CG) method to automatically identify boundary water fluxes in fixed oil reservoir with arbitrary geometry.
引文
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