Integral equation based wellbore preconditioner for 3D electromagnetic response modeling

Modeling subsurface controlled-source electromagnetic (CSEM) responses using the finite-element (FE) method is challenging in the presence of highly conductive wellbore casing. The large conductivity contrast between the casing and the host formation leads to increased computation time and potentially unstable solutions. We address this difficulty by preconditioning a FE solver with an integral equation (IE) primary solution that captures the CSEM response of a realistic-sized steel wellbore casing. Our hybrid IE-FE approach solves the primary field solution using 2-D integral-equation forward modeling and then interpolates the IE-computed solution onto the nodes of a FE mesh. Then using an existing FE simulator, we solve for secondary electric and magnetic field solutions. This approach removes the need for an ultra-fine FE mesh around the wellbore, thereby improving FE solution stability while greatly reducing FE computation time. Our method is illustrated by modeling the CSEM responses of idealized fluid-bearing zones.