基于二次规划的双感应测井反演方法

Inversion method of dual induction log based on quadratic programming

双感应电阻率反演由信号褶积测量原理,通过反褶积或正则化等线性方程组求解获得地层真实电阻率,对于准确求取储层含水饱和度具有重要意义。但传统的反褶积方法无法做到反褶积因子的准确计算,而Tikhonow正则化反演方法出现正则参数选择困难等问题。将反演问题转化为二次规划优化求解,并施加等式约束条件,可保证反演电阻率曲线的光滑性。目的针对等式约束的二次规划问题求解,方法本文基于神经计算原理和时间依赖的非线性动力系统,构造二次规划问题的递归人工神经网络模型,并采用改进Euler法同时模拟求解该模型的最优解和对偶问题解。结果现场实际应用表明,反演的地层电阻率有助于精准判断油、水层,相比原始测量电阻率,更加符合试油结果。结论基于二次规划的地层电阻率反演能够实现对地层原始电阻率的有效反演,具有较强的发现和识别油气储层的能力,可为油田的增储上产提供重要的技术支撑。

Based on signal convolutional measurement,true resistivity of zones is acquired through deconvolution and regularization,which is very important for the calculation of water saturation of reservoirs by dual induction resistivity inversion.It is not feasible to accurately calculate the deconvolution factor by traditional deconvolution methods,and it is diffcult to select regularization parameters in Tikhonov regularization.The inversion problem was converted into an optimization problem of quadratic programming to be solved,and equation constraints were imposed to guarantee the smoothness of the inversed resistivity curves.Objectives For solving the quadratic programming(QP)problem with equation constraints,Methods a recursive artificial neural network model of QP was constructed in this paper based on neurocomputing theory and a timedependent nonlinear dynamical system.The improved Euler method was adopted for numerical simulation to obtain the optimal solution and dual solution of the model simultaneously.Results Factual applications onsite showed that the formation resistivity curves were very helpful in determining oil or water zones accurately and were more coincident with well testing results compared with raw measured resistivity curves.Conclusions The formation resistivity inversion based on quadratic programming effectively reconstructed the original formation resistivity and had a strong capability to discover and identify oil and gas reservoirs.This method provided significant technical support for increasing oil reserves and production.