An improved TSVD-GCV inversion algorithm of pore size distribution in time-domain induced polarization using migration Hankel matrix

Abstract

Reservoir porosity obtained from time-domain induced polarization (TDIP) well logging plays a vital role in estimating the hydraulic properties and obtain the reservoir parameters in a water-flood oil-field. Improving the inversion accuracy of the reservoir porosity can enhance the oil recovery in the water-flood oil-filed. Evaluating reservoir pore size distribution through induced polarization decay curve is confronted with the problems of poor applicability of data pre-processing, low accuracy and lacking of evaluation criteria for inversion results of pore size distribution. The basic principles of TDIP are introduced and the relationship between pore relaxation time and pore diameter is given. Combining the mathematical characteristics of polarization decay curve data, the performance and the limitations of existing pre-processing algorithms are analyzed and pointed out, respectively. An improved data pre-processing algorithm using the spatial characteristics of linear transformation based on migration Hankel matrix is proposed, and this method improves the inversion accuracy of pore size distribution greatly. In the engineering application, 2-logarithmic sampling method is proposed to sample the polarization decay data for more efficient petroleum exploration with less sample points. The different regularization methods, regularization matrix and regularization parameter determination methods are compared and analyzed for the inversion of the pore size distribution. The numerical simulation experimental results show that the stability and accuracy of Truncated Singular Value Decomposition - Generalized Cross Validation (TSVD-GCV), Truncated Singular Value Decomposition - L Curve (TSVD-L) and Tikhonov-I-L are appropriate for the inversion of pore size distribution. Because of the truth that the pore size distribution of rock is unknown, Backus-Gilbert (BG) theory is introduced to evaluate the inversion results of rock polarization decay curve data of a mining area in Jilin Province. The rock sample experiment shows that the TSVD-GCV inversion algorithm has the best performance.