基于地质约束的感应测井非线性正反演研究
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摘要
地层电阻率参数能定性划分油、气、水层，定量评价含油饱和度，是测井解释评价油气藏的主要依据。感应测井能用于测量裸眼井和油基泥浆井中的电阻率。开展感应测井正反演研究能分析不同地层条件下感应测井曲线响应特征，并由感应测井曲线直接获取地层电阻率分布模型。
本文利用频率域有限差分方法实现了二维和三维各向同性地层中感应测井的正演算法，该正演算法首先采用等效源将电磁场分为背景场和散射场以克服测井中发射线圈和接收线圈相距很近导致的计算困难，然后采用LIN预条件方法将散射场进一步分为无旋场和无散场，采用交错网格有限差分对求解区域离散得到大型复系数稀疏线性方程组(Ax=b)，用不完全LU分解和不完全Cholesky分解预条件拟稳定双共轭梯度法求解该线性方程组得到散射场分布，进而求得总场分布，最后由感应测井理论计算出感应测井正演曲线。通过与解析解、数值模式匹配算法数值结果对比，验证该正演算法的有效性。
在分析差分进化（DE）和粒子群优化（PSO）非线性全局最优化智能算法原理的基础上，研究影响两个算法收敛速度和全局搜索能力的因素，有针对性提出DE算法和PSO算法的改进措施。在此基础上，综合考虑DE和PSO算法优缺点，提出差分进化粒子群（DEPSO）混合最优化算法。通过一组标准测试函数测试本文提出的DEPSO的性能，数值实验结果表明，该DEPSO算法具有较高的收敛速度和很强的全局搜索能力，特别适合于多峰值函数极值问题求解。
提出基于DEPSO的感应测井反演算法，该反演算法充分利用DEPSO算法的全局搜索能力，同时利用先验地质信息构造正则化约束项，克服感应测井反演的不稳定性和非唯一性困难。利用几个理论模型考察该反演算法的有效性，在无噪声情况下，能准确反演出真实模型参数，随着反演参数增多和观测数据噪声增大，反演精度有所下降。理论模型反演结果表明，本文提出的感应测井反演算法具有不依赖于初始模型、不需要被优化目标函数的梯度信息和很强的全局搜索能力的优点。该算法能较好克服观测数据不足和观测数据误差造成的反演问题不适定性，适用于非线性、多参数和多极值的地球物理反演问题。实测资料反演结果表明，本反演方法能从感应测井曲线中反演出符合地下真实情况的地层真电导率模型，为进一步测井解释与评价提供可靠的依据。
The formation resistivity, which can be used to distinguish the oil, gas and waterlayers qualitatively and to evaluate the oil saturation quantitatively, is the main basisfor logging interpretation and evaluation of the oil and gas reservoirs. The inductionlogging tools can be used for measuring the formation resistivity in the boreholes andoil-based mud wells. We can analysis the logging response characteristics of differentformation by forward modeling, and can obtain the formation resistivity from theinduction logging directly by inversion.
In this dissertation, the finite difference frequency-domain method is employedfor modeling the induction logging in 2D and 3D isotropic formation. The scatteredfield formulation is used because transmitter coils and receiver coils are often locatedvery close in well logging application. This dissertation employs the LIN preconditiontechnique to decompose the scattered field into curl-free and divergence-freeprojection. After finite-differencing the equations for the scattered field, the linearsystem (Ax=b) is assembled, and it is solved with Bi-Conjugate Gradient Stabilized(BICGSTAB) methods with incomplete LU factorization and incomplete Choleskyfactorization preconditioning. When the total electromagnetic field is determined, theinduction logging response is calculated based on the induction logging theorem. Theforward algorithm is verified by contrasting the numerical results with those of theanalytical solution and numerical mode-match method.
In this dissertation, the influencing factors of the convergence speed and globalsearch capacity of the differential evolution (DE) and particle swarm optimization(PSO) algorithm are studied and several improvements of the DE and PSO algorithmare proposed, after studying the principle of the DE and PSO algorithm. A novel DEand PSO hybrid algorithm (DEPSO) is developed considering the advantages anddisadvantages of both DE and PSO. The DEPSO algorithm is evaluated on severalbenchmark functions. The numerical results indicate that the DEPSO algorithm hasthe advantages of fast convergence and fine global search capacity, and it is suitablefor the multi-modal function optimization.
Based on the DEPSO algorithm which has the advantage of fine global searchcapacity, an inversion algorithm for induction logging is developed which employsthe regularization method to stabilize the inversion with the prior geologicalinformation. The numerical results show that with this inversion algorithm, the modelparameters can be inversed accurately from the noise free induction logging data, andwhen the unknown parameters and the noise of observed data increase, the inversionaccuracy decreases. The inversion results of the synthetic data indicate that theDEPSO inversion algorithm has the advantages of independence of the initial valuesand fine global search capacity. It can overcome the ill-posed problem caused by theinsufficiency and mistake of the observed data, and can be applied to solve thenonlinear multi-parameters multi-modal geophysics inversion problems. Theinversion results of field induction logging data indicate that the real conductivitymodel of the formation can be obtained with the DEPSO inversion algorithm. Themodel accords to the actual subsurface situation and can be used as the basis of thewell logging interpretation and evaluation.
本文利用频率域有限差分方法实现了二维和三维各向同性地层中感应测井的正演算法，该正演算法首先采用等效源将电磁场分为背景场和散射场以克服测井中发射线圈和接收线圈相距很近导致的计算困难，然后采用LIN预条件方法将散射场进一步分为无旋场和无散场，采用交错网格有限差分对求解区域离散得到大型复系数稀疏线性方程组(Ax=b)，用不完全LU分解和不完全Cholesky分解预条件拟稳定双共轭梯度法求解该线性方程组得到散射场分布，进而求得总场分布，最后由感应测井理论计算出感应测井正演曲线。通过与解析解、数值模式匹配算法数值结果对比，验证该正演算法的有效性。
在分析差分进化（DE）和粒子群优化（PSO）非线性全局最优化智能算法原理的基础上，研究影响两个算法收敛速度和全局搜索能力的因素，有针对性提出DE算法和PSO算法的改进措施。在此基础上，综合考虑DE和PSO算法优缺点，提出差分进化粒子群（DEPSO）混合最优化算法。通过一组标准测试函数测试本文提出的DEPSO的性能，数值实验结果表明，该DEPSO算法具有较高的收敛速度和很强的全局搜索能力，特别适合于多峰值函数极值问题求解。
提出基于DEPSO的感应测井反演算法，该反演算法充分利用DEPSO算法的全局搜索能力，同时利用先验地质信息构造正则化约束项，克服感应测井反演的不稳定性和非唯一性困难。利用几个理论模型考察该反演算法的有效性，在无噪声情况下，能准确反演出真实模型参数，随着反演参数增多和观测数据噪声增大，反演精度有所下降。理论模型反演结果表明，本文提出的感应测井反演算法具有不依赖于初始模型、不需要被优化目标函数的梯度信息和很强的全局搜索能力的优点。该算法能较好克服观测数据不足和观测数据误差造成的反演问题不适定性，适用于非线性、多参数和多极值的地球物理反演问题。实测资料反演结果表明，本反演方法能从感应测井曲线中反演出符合地下真实情况的地层真电导率模型，为进一步测井解释与评价提供可靠的依据。
The formation resistivity, which can be used to distinguish the oil, gas and waterlayers qualitatively and to evaluate the oil saturation quantitatively, is the main basisfor logging interpretation and evaluation of the oil and gas reservoirs. The inductionlogging tools can be used for measuring the formation resistivity in the boreholes andoil-based mud wells. We can analysis the logging response characteristics of differentformation by forward modeling, and can obtain the formation resistivity from theinduction logging directly by inversion.
In this dissertation, the finite difference frequency-domain method is employedfor modeling the induction logging in 2D and 3D isotropic formation. The scatteredfield formulation is used because transmitter coils and receiver coils are often locatedvery close in well logging application. This dissertation employs the LIN preconditiontechnique to decompose the scattered field into curl-free and divergence-freeprojection. After finite-differencing the equations for the scattered field, the linearsystem (Ax=b) is assembled, and it is solved with Bi-Conjugate Gradient Stabilized(BICGSTAB) methods with incomplete LU factorization and incomplete Choleskyfactorization preconditioning. When the total electromagnetic field is determined, theinduction logging response is calculated based on the induction logging theorem. Theforward algorithm is verified by contrasting the numerical results with those of theanalytical solution and numerical mode-match method.
In this dissertation, the influencing factors of the convergence speed and globalsearch capacity of the differential evolution (DE) and particle swarm optimization(PSO) algorithm are studied and several improvements of the DE and PSO algorithmare proposed, after studying the principle of the DE and PSO algorithm. A novel DEand PSO hybrid algorithm (DEPSO) is developed considering the advantages anddisadvantages of both DE and PSO. The DEPSO algorithm is evaluated on severalbenchmark functions. The numerical results indicate that the DEPSO algorithm hasthe advantages of fast convergence and fine global search capacity, and it is suitablefor the multi-modal function optimization.
Based on the DEPSO algorithm which has the advantage of fine global searchcapacity, an inversion algorithm for induction logging is developed which employsthe regularization method to stabilize the inversion with the prior geologicalinformation. The numerical results show that with this inversion algorithm, the modelparameters can be inversed accurately from the noise free induction logging data, andwhen the unknown parameters and the noise of observed data increase, the inversionaccuracy decreases. The inversion results of the synthetic data indicate that theDEPSO inversion algorithm has the advantages of independence of the initial valuesand fine global search capacity. It can overcome the ill-posed problem caused by theinsufficiency and mistake of the observed data, and can be applied to solve thenonlinear multi-parameters multi-modal geophysics inversion problems. Theinversion results of field induction logging data indicate that the real conductivitymodel of the formation can be obtained with the DEPSO inversion algorithm. Themodel accords to the actual subsurface situation and can be used as the basis of thewell logging interpretation and evaluation.
引文
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