New Theory of Flight
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When trying to obtain a better characterization of the Earth's subsurface, it is common to use borehole through-casing resistivity measurements. It is also common for the wells to be surrounded by a metal casing to protect the well and avoid possible collapses. The presence of this metal case highly complicates the numeric simulation of the problem due to the high conductivity of the casing compared to the conductivity of the rock formations. Here we present an application of some theoretical asymptotic methods in order to deal with complex borehole scenarios like cased wells. The main idea consist in replacing the part of the domain related to the casing by a transmission impedance boundary condition. The small thickness of the casing makes it ideal to apply this kind of mathematical technique. When eliminating the casing from the computational domain, the computational cost of the problems considerably decreases, while the effect of the casing does not disappear due to the impedance transmission conditions. The results show that when applying an order three impedance boundary condition for a simplified domain, it only generates a negligible approximation error, while it considerably reduces the computational cost.