核磁共振T2谱反演及流体识别评价方法研究
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摘要
提出两种核磁共振T2谱反演方法:共轭梯度法和M-P广义逆法。共轭梯度法首先建立反演的目标函数,然后利用共轭梯度法具有二次终止性、收敛速度快的特点求该目标函数的极小值从而得到T2谱,采用迭代和平方两种方法实现T2谱的非负约束;M-P广义逆法首先推导出T2谱反演的M-P广义逆解,然后采用截断法或阻尼法使反演结果稳定,并应用迭代技术进行T2谱的非负约束。数值实验及岩心和测井的实际应用表明:共轭梯度法和M-P广义逆法都可以有效地应用于岩心数据和测井资料的T2谱反演中;共轭梯度法可用于信噪比SNR≥5的T2谱反演,但迭代约束速度慢,平方约束容易陷入局部极小;M-P广义逆法可用于SNR≥10的双峰谱和SNR≥20的三峰谱反演,对于测井的多点连续反演只需进行一次奇异值分解,反演速度比共轭梯度法大为提高。
分析T2谱反演的影响因素:回波采集参数及质量(回波间隔、回波个数、回波采集时间、信噪比)、T2谱反演设置参数(布点个数、布点范围)和T2谱形态(单峰、双峰、三峰),给出反演质量评价与控制的指标:条件数、回波数据分辨矩阵、T2谱参数分辨矩阵、展伸系数和方差。应用数值实验和质量评价与控制指标研究了上述各种因素对反演质量的影响,指出提高反演质量的途径,指导岩心核磁共振实验和核磁共振测井的测前设计。
基于CPMG和DE脉冲序列,提出核磁共振储层流体一维T2谱分离方法。该方法首先建立储层岩石多流体弛豫模型,然后采用稳健的反演技术从CPMG和DE脉冲序列测量的多组回波数据中分离反演出无扩散水T2谱(表面弛豫谱)、无扩散油T2谱(自由弛豫谱)和扩散气T2谱(扩散弛豫谱)。该方法在油气水T2谱重合的情况下仍可以分离出各自的T2谱,克服了常规核磁共振流体识别方法(TDA和DIFAN)只针对视谱(油气水混合谱)解释计算的缺陷。不同含水饱和度的油水和气水两相正反演数值实验表明:反演的无扩散水T2谱、无扩散油T2谱和扩散气T2谱与构造的T2谱符合得很好。因此该方法在理论上是可行的,可以进一步应用于实验室和测井的流体识别与评价工作中,检验其实用性。
Conjugate gradient method and M-P generalized inverse method of NMR T2 spectrum inversion are proposed in this thesis. Conjugate gradient method builds up the inversion objective function at first, then searches the minimum of the objective function with the conjugate gradient algorithm that has quick convergence rate and quadratic termination,and puts Non-negativity constraint of T2 spectrum into practice by way of iteration and square at last. M-P generalized inverse method deduces the solution of M-P generalized inverse of the T2 spectrum inversion at first, then The stability and resolution of the solution are ensured by discarding some small singular values or adding damping term, finally, the non-negativity constraint of T2 spectrum is realized by iterative technique. Numerical simulation and practical application of core and log demonstrates:Both methods can be applied in T2 spectrum inversion of drilling core and well logging effectively; Conjugate gradient method can be used in the situation of the signal to noise ratio(SNR)≥5,but iteration non-negativity constraint is slow and square non-negativity constraint is easy to fall into local minimum of the function; M-P generalized inverse method can be applied in bimodal spectrum of SNR≥10 and trimodal spectrum of SNR≥20, its inversion velocity is larger than Conjugate gradient method in the inversion of log because it need singular value decomposition(SVD) once only as to continuous logging data.
There are several influential factors of T2 spectrum inversion:Quality and parameters of echoes acquisition that include echo spacing,echo numbers, acquisition time and SNR, Presupposition parameters of inversion that include numbers and range of T2 value, shape of T2 spectrum that include single modal,bimodal and trimodal distribution. Quality evaluation and control indices of T2 spectrum inversion that include conditional number, echo data resolution matrix, T2 spectrum parameter resolution matrix, spread coefficient and variance are proposed. All kinds of influential factors above mentioned are studied applying numerical simulation and evaluation and control indices of quality.Approaches to improve quality of inversion are suggested so that they can direct prelog designing of core experiment and well logging.
The method of NMR one-dimension T2 spectrum separation of reservoir fluid is proposed based on CPMG and DE(Difussion Editing) pulse sequence. It builds up multi-fluid relaxation model of Oil-Water and Gas-Water of reservoir firstly. Then non-difussion water T2 spectrum (surface relaxation spectrum), non-difussion oil T2 spectrum (bulk relaxation spectrum) and gas T2 spectrum (difussion relaxation spectrum) are inverted from several echo trains which come from CPMG and DE pulse sequence by robust inversion technique. By this method conincidence T2 spectrum of oil, gas and water can be separated from each one. It overcomes the defect of conventional fluid identification methods (TDA and DIFAN), which interpret and calculate apparent spectrum(composite spectrum of oil,gas and water). Forward and inverse numerical experiment from different water saturation in two phases of Oil-Water and Gas-Water shows that the inversion of non-difussion water T2 spectrum, non-difussion oil T2 spectrum and difussion gas T2 spectrum accord with those of artificial spectrum respectively well. So this method is feasible theoretically. Its practicability can be verified further by being used in identification and evaluation of reservoir fluid in laboratory and well logging.
分析T2谱反演的影响因素:回波采集参数及质量(回波间隔、回波个数、回波采集时间、信噪比)、T2谱反演设置参数(布点个数、布点范围)和T2谱形态(单峰、双峰、三峰),给出反演质量评价与控制的指标:条件数、回波数据分辨矩阵、T2谱参数分辨矩阵、展伸系数和方差。应用数值实验和质量评价与控制指标研究了上述各种因素对反演质量的影响,指出提高反演质量的途径,指导岩心核磁共振实验和核磁共振测井的测前设计。
基于CPMG和DE脉冲序列,提出核磁共振储层流体一维T2谱分离方法。该方法首先建立储层岩石多流体弛豫模型,然后采用稳健的反演技术从CPMG和DE脉冲序列测量的多组回波数据中分离反演出无扩散水T2谱(表面弛豫谱)、无扩散油T2谱(自由弛豫谱)和扩散气T2谱(扩散弛豫谱)。该方法在油气水T2谱重合的情况下仍可以分离出各自的T2谱,克服了常规核磁共振流体识别方法(TDA和DIFAN)只针对视谱(油气水混合谱)解释计算的缺陷。不同含水饱和度的油水和气水两相正反演数值实验表明:反演的无扩散水T2谱、无扩散油T2谱和扩散气T2谱与构造的T2谱符合得很好。因此该方法在理论上是可行的,可以进一步应用于实验室和测井的流体识别与评价工作中,检验其实用性。
Conjugate gradient method and M-P generalized inverse method of NMR T2 spectrum inversion are proposed in this thesis. Conjugate gradient method builds up the inversion objective function at first, then searches the minimum of the objective function with the conjugate gradient algorithm that has quick convergence rate and quadratic termination,and puts Non-negativity constraint of T2 spectrum into practice by way of iteration and square at last. M-P generalized inverse method deduces the solution of M-P generalized inverse of the T2 spectrum inversion at first, then The stability and resolution of the solution are ensured by discarding some small singular values or adding damping term, finally, the non-negativity constraint of T2 spectrum is realized by iterative technique. Numerical simulation and practical application of core and log demonstrates:Both methods can be applied in T2 spectrum inversion of drilling core and well logging effectively; Conjugate gradient method can be used in the situation of the signal to noise ratio(SNR)≥5,but iteration non-negativity constraint is slow and square non-negativity constraint is easy to fall into local minimum of the function; M-P generalized inverse method can be applied in bimodal spectrum of SNR≥10 and trimodal spectrum of SNR≥20, its inversion velocity is larger than Conjugate gradient method in the inversion of log because it need singular value decomposition(SVD) once only as to continuous logging data.
There are several influential factors of T2 spectrum inversion:Quality and parameters of echoes acquisition that include echo spacing,echo numbers, acquisition time and SNR, Presupposition parameters of inversion that include numbers and range of T2 value, shape of T2 spectrum that include single modal,bimodal and trimodal distribution. Quality evaluation and control indices of T2 spectrum inversion that include conditional number, echo data resolution matrix, T2 spectrum parameter resolution matrix, spread coefficient and variance are proposed. All kinds of influential factors above mentioned are studied applying numerical simulation and evaluation and control indices of quality.Approaches to improve quality of inversion are suggested so that they can direct prelog designing of core experiment and well logging.
The method of NMR one-dimension T2 spectrum separation of reservoir fluid is proposed based on CPMG and DE(Difussion Editing) pulse sequence. It builds up multi-fluid relaxation model of Oil-Water and Gas-Water of reservoir firstly. Then non-difussion water T2 spectrum (surface relaxation spectrum), non-difussion oil T2 spectrum (bulk relaxation spectrum) and gas T2 spectrum (difussion relaxation spectrum) are inverted from several echo trains which come from CPMG and DE pulse sequence by robust inversion technique. By this method conincidence T2 spectrum of oil, gas and water can be separated from each one. It overcomes the defect of conventional fluid identification methods (TDA and DIFAN), which interpret and calculate apparent spectrum(composite spectrum of oil,gas and water). Forward and inverse numerical experiment from different water saturation in two phases of Oil-Water and Gas-Water shows that the inversion of non-difussion water T2 spectrum, non-difussion oil T2 spectrum and difussion gas T2 spectrum accord with those of artificial spectrum respectively well. So this method is feasible theoretically. Its practicability can be verified further by being used in identification and evaluation of reservoir fluid in laboratory and well logging.
引文
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