Estimation of Reservoir Parameters From Inversion of Triaxial Induction Data Constrained by Mud-Filtrate Invasion Modeling
Mud-filtrate invasion happens commonly during the drilling and has a great effect on the triaxial induction logging data. A good description of the invasion can help achieve a better understanding of the formation. A mud-filtrate invasion constrained inversion approach is thus introduced to simultaneously invert for the sand fraction ( <inline-formula><tex-math notation="LaTeX">$F_{\text{sand}}$</tex-math></inline-formula>), irreducible water saturation (<inline-formula><tex-math notation="LaTeX">$S_{\text{wr}}$</tex-math></inline-formula>), and average invasion rate ( <inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula>) with the triaxial induction logging data in anisotropic laminated sand–shale formations. In the inversion, the dynamic mud-filtrate invasion is modeled to account for the invasion effect. The invasion modeling provides the profiles of water saturation and salt concentration, which can be used to obtain the conductivity in the sand formation through a saturation-conductivity model (e.g., Archie's law). The anisotropic resistivities <inline-formula><tex-math notation="LaTeX">$R_h$ </tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$R_v$</tex-math></inline-formula> of the laminated sand–shale formation can then be calculated by the anisotropic bimodal system based on the obtained sand conductivity and the shale anisotropic resistivities <inline-formula><tex-math notation="LaTeX"> $R_{\text{shale}{,}h}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX"> $R_{\text{shale}{,}v}$</tex-math></inline-formula>. The triaxial induction logging is finally modeled with <inline-formula><tex-math notation="LaTeX">$R_h$</tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$R_v$</tex-math></inline-formula>. By matching the calculated logging data with the measured data, the unknowns <inline-formula><tex-math notation="LaTeX">$F_{\text{sand}}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">$S_{\text{wr}}$</tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$q$</tex-math></inline-formula> can be estimated. A quantitative evaluation of the new inversion scheme is performed with the triaxial induction tool Rt Scanner. The synthetic data without noise and with 2% white Gaussian noise are used. From the inversion tests, we observe that the sand fraction and irreducible water saturation can be well estimated by the long-offset measurements, which are less affected by the mud-filtrate invasion in the scenario that the invasion is not deep. In contrast, the short-offset measurements are more sensitive to the average invasion rate, since the detection range of these measurements is in the vicinity of the borehole. In the inversion, the sand fraction, irreducible water saturation, and average invasion rate are estimated simultaneously. The good agreement between the estimated results with their true values demonstrates the effectiveness of the invasion constrained inversion scheme.