用迭代反演算法进行二维井间电磁成像

魏宝君，张中庆，张庚骥．用迭代反演算法进行二维井间电磁成像．测井技术，１９９８，２２（６）：４０７～４１１提出了一种基于逐次逼近解法的迭代反演算法对井间地层电导率的构造进行成像。该方法应用一阶Ｂｏｒｎ近似将积分方程线性化，得到对电导率分布的初始估计，在迭代反演中应用高阶Ｂｏｒｎ近似对井间地层电导率构造作更精确的估计。数值计算结果表明，这种迭代反演算法与基于Ｂｏｒｎ近似、二阶Ｂｏｒｎ近似和扩展Ｂｏｒｎ近似的反演算法相比提高了成像分辨率，而计算效率相当。应用该方法还可以对井间电导率分布进行二次成像。

二维井间电磁场的正反演计算

提出了一种改进的逐次逼近解法 ,并用该方法对轴对称二维井间电磁场进行了正反演计算。与逐次逼近解法相比 ,该方法收敛性强 ,应用范围广 ,可适用于高电导率对比地层。与直接求解积分方程相比 ,由于不必进行直接的大型复矩阵求逆运算 ,该方法计算速度快 ,所需内存少。反演中采用了Born迭代算法 ,将成像区域集中于一定范围内。考虑到信息量和计算机内存的限制 ,采用双重面元分割法 ,将反演区域分割为一定数目的大面元 ,每个大面元被分割为几个小面元。属于同一大面元的不同小面元具有不同的磁矢势 ,但具有相同的电导率 ,从而减少了反演过程中未知量的数目。根据第一次成像结果确定出更准确的成像范围 ,并进行第二次成像。数值计算结果表明 ,改进的逐次逼近解法是计算二维井间电磁场的一种有效方法 ,将该方法用于反演过程能够得到较高分辨率的二维井间电导率图像。

用改进的逐次逼近解法计算二维井间电磁场

提出了一种计算积分方程的新方法——改进的逐次逼近解法 (MSAM) ,并用该方法计算了轴对称二维井间电磁场。与传统的逐次逼近解法 (SAM)相比 ,该方法收敛性强 ,应用范围广 ,可适用于高电导率对比地层。由于不必进行直接的大型矩阵求逆运算 ,因此与积分方程的直接解法 (IE)相比 ,该方法计算速度更快 ,所需内存更少。采用矩阵求逆方法计算了成层介质中的二维 Green函数 ,并对含 Green函数的积分进行了简化 ,从而加快了计算速度。数值计算结果显示 ,在地层电导率对比度达到 2个数量级时 MSAM仍收敛 ,且计算结果与直接求解积分方程的结果一致 ,因此

傍河三维与二维井流的电模拟对比试验研究

本文采用连续介质水电比拟法,对不完整河旁三维井流与完整河旁二维井流作了对比研究。结果表明,当其他条件相同时,前者水井出水量只能达到后者出水量的80％左右;实测的两类流场图,显示出三维井流与二维井流的许多重要特征和区别,对此作了详细对比分析,阐明了流量显著变小的机理;指出不完整河旁井流问题按三维流计算的必要性;对当前工作提出了重要且可行的建议。

二维非线性井流问题解析解研究

在均质等厚、水平各向同性而竖向异性、无限分布的承压含水层中,以定流量抽水,根据水量平衡原理,建立了二维非线性水流运动方程,并针对确定的非线性渗流规律,用Boltzmann变换对方程进行了求解,推导出了二维非线性井流问题渗流速度和水头降深的解析表达式。

变附加应力条件下考虑桩体二维井阻作用的复合地基固结解析理论研究

通过在现有解的形式基础上增加一个二次多项式,提出一种新的复合地基固结解的形式及解答方法,推导得到地基附加应力既随时间变化也随深度变化条件下考虑桩体竖向及径向二维井阻作用的散体材料桩复合地基固结解析解,通过退化、与已有解的比较等方法对解进行分析验证。结果表明,现有的瞬时荷载下考虑桩体径竖向渗流的解、考虑桩体竖向渗流与变形协调的解、太沙基一维固结解等都是本文解的特例,这说明本文解的正确合理性。地基加载历时越长,固结越慢;地基底部附加应力越小,固结越快;考虑桩体径竖向二维井阻时地基固结比只考虑竖向井阻时慢,桩径比越小,桩体渗透系数越小,两者的差异越大。本文解的表达形式及解答方法,为复合地基固结度的求解提供一种新的思路,发展和完善了现有的复合地基固结理论。

Numerical simulation of(T_2,T_1) 2D NMR and fluid responses

One-dimensional nuclear magnetic resonance （1D NMR） logging technology is limited for fluid typing, while two-dimensional nuclear magnetic resonance （2D NMR） logging can provide more parameters including longitudinal relaxation time （71） and transverse relaxation time （T2） relative to fluid types in porous media. Based on the 2D NMR relaxation mechanism in a gradient magnetic field, echo train simulation and 2D NMR inversion are discussed in detail. For 2D NMR inversion, a hybrid inversion method is proposed based on the damping least squares method （LSQR） and an improved truncated singular value decomposition （TSVD） algorithm. A series of spin echoes are first simulated with multiple waiting times （Tws） in a gradient magnetic field for given fluid models and these synthesized echo trains are inverted by the hybrid method. The inversion results are consistent with given models. Moreover, the numerical simulation of various fluid models such as the gas-water, light oil-water, and vicious oil-water models were carried out with different echo spacings （TEs） and Tws by this hybrid method. Finally, the influences of different signal-to-noise ratios （SNRs） on inversion results in various fluid models are studied. The numerical simulations show that the hybrid method and optimized observation parameters are applicable to fluid typing of gas-water and oil-water models.

Comparison of different inversion methods of D-T_(2)two-dimensional nuclear magnetic resonance logging and applicability analysis

D-T_(2)two-dimensional nuclear magnetic resonance(2D NMR)logging technology can distinguish pore fluid types intuitively,and it is widely used in oil and gas exploration.Many 2D NMR inversion methods(e.g.,truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization methods)have been proposed successively,but most are limited to numerical simulations.This study focused on the applicability of different inversion methods for NMR logging data of various acquisition sequences,from which the optimal inversion method was selected based on the comparative analysis.First,the two-dimensional NMR logging principle was studied.Then,these inversion methods were studied in detail,and the precision and computational efficiency of CPMG and diffusion editing(DE)sequences obtained from oil-water and gas-water models were compared,respectively.The inversion results and calculation time of truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization were compared and analyzed through numerical simulations.The inversion method was optimized to process SP mode logging data from the MR Scanner instrument.The results showed that the TIST-regularization and LM-norm smoothing methods were more accurate for the CPMG and DE sequence echo trains of the oil-water and gas-water models.However,the LM-norm smoothing method was less time-consuming,making it more suitable for logging data processing.A case study in well A25 showed that the processing results by the LM-norm smoothing method were consistent with GEOLOG software.This demonstrates that the LM-norm smoothing method is applicable in practical NMR logging processing.