The Response Of Multiarray Induction Tools In Highly Dipping Formations With Invasion And In Arbitrary 3D Geometries

With the rapid expansion of horizontal drilling, the interpretation of logs, especially resistivity logs, has become a serious problem. The proximity of shale layers or of water legs can seriously affect deep resistivity logs, and invasion can seriously affect shallow resistivity logs. The current state of affairs is that determining Rt in a horizontal or very high angle well is often impossible. Modeling techniques are now available for solving the full 3D problem necessary for deviated well interpretation. We have developed such a 3D modeling code and applied it to improve the interpretation of multiarray induction tool response. The code uses the Lanczos spectral-decomposition method to solve Maxwell?s equations on a staggered finite-difference grid. The finite-difference code has been benchmarked against analytical solutions for subsets of the 3D geometry, and agreement is within 3%. When run on a parallel machine, 50 ft of 3D log can be generated in under 6 hours. The code takes into account dipping beds and unsymmetrical invasion at the same time, as well as resistivity anisotropy. Several horizontal well interpretation problems have been investigated with the code. One is the case of axisymmetric cylindrical invasion in a permeable zone below a cap shale interface. In this case modeling shows that for shallow invasion, the deepest Array Induction Imager tool curves can be used to infer and proximity to the shale cap, while the shallowest curve indicates Rxo. If deeper invasion is modeled, only the deepest induction curve indicates Rt, while several of the shallow curves read Rxo The code has also been used to model non-circular invasion fronts caused by either permeability anisotropy or buoyancy segregation typical in highly deviated wells. Both cases are characterized by a considerable quantity of filtrate shunted away from the well in preferential directions, resulting in less invading fluid near the wellbore. As a consequence, there is an increase of the influence of Rt on the shallow AlT logs. These cases indicate that induction logs in complex formations still have geometrical interpretations, but that they are different than interpretations used in vertical wells. A log example illustrates the power of 3D modeling in interpreting multiarray induction logs in difficult wells. In a horizontal well with moderately salty invasion, modeling shows that a large separation between the deepest induction curves is caused by a combination of invasion effects and polarization horns near a cap shale. In addition, an annulus is present to complicate interpretation.