Borehole effect of the Tri-axial Array Coplanar System in Anisotropic Formation

The tri-axial array induction logging instrument measures nine distinct components tensor conductivity, unveiling detailed the intricate anisotropic characteristics of the formation. In this paper, we derive the electromagnetic field expressions of the magnetic dipole in anisotropic formation. Then, analyze the borehole effect response characteristics of the tri-axial coplanar system in anisotropic formation under different borehole diameters and various formation vertical and horizontal conductivities. The results show that with fixed formation and mud conductivities, subarray 1 apparent conductivity increases approximately linearly with increasing borehole diameter, and the borehole diameters effects of subarrays 7 and 8 are small and negligible. In a standard 8in borehole, when both mud and formation vertical conductivities change simultaneously, the borehole effects of different conductivity contrast and different spacing coplanar systems are observed. The borehole effect of subarray 8 is small when the formation vertical conductivity is less than 1.38S/m, but the nonlinearity is significant when the formation vertical conductivity is greater than 1.38S/m. As the formation horizontal conductivity increases, the short subarrays increase approximately linearly, and with increasing spacing, the skin effect is serious, resulting in a pronounced nonlinearity. When the formation horizontal conductivity is greater than 1.12S/m, the apparent conductivity of subarray 8 decreases almost linearly with the increase of formation horizontal conductivity, indicating that the measurement range of the horizontal conductivity of the tri-axial array induction coplanar system is smaller than that of the vertical conductivity. The research lays a theoretical basis for the development of the tri-axial induction logging tool.