On the Simulation of Well-Logging Tools for Oil and Gas Exploration Using Unconditionally Stable Time-Domain FDTD Algorithms

Electromagnetic well logging tools are traditionally used in oil and gas exploration to measure resistivities of the surrounding earth formation. The cylindrical finite-difference time domain (FDTD) method has been popularly applied to solve well logging tool problems because of its matrix-free characteristic and its flexibility to simulate complex geometries. However, the maximum time step in FDTD is limited by the CFL condition, leading to the need of a large number of time steps in highly refined grids. To overcome the CFL condition, an unconditionally stable alternating-direction-implicit (ADI)-FDTD method can be employed. However, ADI-FDTD exhibits increased numerical dispersion errors for large time steps. To reduce the dispersion error, a complex envelope (CE) ADI-FDTD algorithm is introduced here in cylindrical coordinates. The proposed algorithm reduces the computation time while maintaining the dispersion error at acceptable levels