Inversion Of Borehole Electromagnetic Data Based On Dispersive Medium

Effect of low-frequency polarization(less than 10 kHz)in the formation has a clear function in measuring the amplitude of the electromagnetic(EM)field,the quadrature resistivity directly shows the effect of low-frequency polarization and has significant influence on electromagnetic fields.The distribution of the in-phase and quadrature electrical resistivity near borehole can be reconstructed based on the borehole electromagnetic data.This information might contribute to monitor of oil saturation and geothermal fields during production through crosshole or borehole-to-surface EM methods.Based on the measurement of eight carbonate reservoir core samples,we inverted the parameters of the empirical rock physical models and designed the complex resistivity models for oil-saturated reservoir.As described later in this article,a complex resistivity imaging method based on frequency-domain electromagnetic inversion was developed.In conclusion,the following results and understandings can be obtained:(1)Electromagnetic dispersion characteristics of carbonate reservoirsBased on the core samples of carbonate buried-hill reservoir,the frequency dependent complex resistivity characteristics were measured and analyzed.The relationship between complex resistivity and oil saturation is discussed.Taking into account the conduction and polarization effect,the Debye model and Cole-Cole model were fitted by using the regularized least squares algorithm,and the induced polarization(IP)effect parameters were extracted.A crosshole electromagnetic survey based on one-dimensional simulation test was carried out to discuss the anomalous contribution of the quadrature resistivity through different frequencies,different spacings of wells and different contrast ratios between the target and background resistivity.The simulation results showed that the measurement of oil-bearing reservoir showed obvious electromagnetic dispersion characteristics.(2)Frequency-domain borehole electromagnetic modelingThis part presented an edge-based finite-element method for numerical modeling of 3D electromagnetic data in the dispersive medium based on the hexahedral element.In the framework of the finite element iteration solving scheme,A spectral equivalent transformation was implemented to the complex linear system.In addition,an incomplete LU decomposition preconditioning method was adopted to improve the efficiency of electromagnetic simulation with multi-source,multi-frequency and multi-model applications.(3)Crosshole electromagnetic inversionBased on the Gauss-Newton inversion framework,the in-phase and quadrature resistivity model were reconstructed from the synthetic crosshole EM data.In the inversion process,a method based on general measurement constraints was employed to improve the reconstruction of model interface feature compared with the smooth constraint inversion.During the inversion iteration,the spectral method based on the Lanczos decomposition was used for solving normal equations corresponding to multiple regularization parameters simultaneously.This provided a rich amount of data for the L-curve method in determining the regularization parameter and greatly improved the efficiency of the inversion.