基于SVD和DE反演方法的渗透率估计

Permeability estimation based on singular value decomposition and differential evolution inversion method

根据孔隙流体离子扩散浓度分布,推导出激发极化弛豫时间与孔隙半径的平方成正比,并与孔隙内溶液的扩散系数相关.在分析信噪比和参变量个数对差分进化(DE)算法反演精度影响的基础上,提出先用奇异值分解(SVD)方法大致确定组分数,再用DE算法反演弛豫谱的联合反演方法,并建立结合弛豫谱、孔隙度和地层因数的综合渗透率估计模型.结果表明:联合反演算法无须事先给定弛豫时间分布,反演精度高,对信噪比鲁棒性好,而且基于弛豫谱的综合估计模型可以显著提高渗透率估计的准确度,其中驰豫时间谱、孔隙度和地层因数的综合模型对于岩心样品的渗透率估计精度可以达到0.980 2.

According to diffusion concentration distribution of pore ions,it was derived that induced polarization relaxation time was in proportion to the square of pore radius,and was related to diffusion coefficient of pore solution.After the influence of signal-to-noise（SNR）and the number of variables on inversion accuracy of differential evolution（DE）algorithm were analyzed,a two-stage relaxation time spectrum（RTS）inversion method was proposed.At first stage,singular value decomposition（SVD）method was used to determine the number of variables,while DE algorithm was applied to obtain accurate solution at second stage.For the permeability estimation,an integrated model with RTS,porosity and formation factor was introduced.The inversion results show that the two-stage inversion method without a given relaxation time distribution in advance,has high inversion accuracy and robustness to SNR and the integrated model with RTS could improve the accuracy of permeability estimation remarkably,especially the accuracy of model based on RTS,porosity and formation factor reaches 0.980 2.