Applications Of Vector Finite Element Method To Simulate Logging While Drilling Resistivity Tools

A novel vector finite element method (FEM) is proposed to simulate logging-while-drilling (LWD) resistivity tool in three dimensional (3D) inhomogeneous medium. In this paper, the response of induction well logging in deviated and horizontal wells have been Studied. The tetrahedral elements based vector finite element method(VFEM) is used to compute electromagnetic fields in 3-D inhomogeneous media with arbitrary distribution of conductivity. Because of the cylindrical symmetry of the well logging system, a cylindrical grid is used for the Simulation. The total field is separated into the background and the secondary fields, which reduce the mesh Size and improve the Simulation accuracy effectively.Layered medium combined with dipping borehole and invaded zones is partitioned into tetrahedrons. Each tetrahedron has six vector edge elements. The number of unknowns can be over 1 million for 3D LWD applications which frontal solver is incapable to solve the discretized equations. In such a scenario, an algebraic multigrid (AMG) method combined with multifrontal solver is developed to solve this very large scale problem with personal computers. The resulting program is validated through published results derived from finite difference time-domain (FDTD) method, and through the borehole measurement data. The code has been used to compute the borehole correction charts, eccentric correction charts, side bed effects, and dipping angle effects for LWD tools.Formation model used in this paper includes the layered structure of hole, in which the hole can be parallel with the ground, vertical or have a certain angle, and logging-while-drilling (LWD) resistivity tool exists in the borehole. A novel vector finite element method (FEM) proposed in this paper with multiple front-line combination of multi-grid method to simulate logging-while-drilling (LWD) resistivity tool in three dimensional (3D) inhomogeneous medium can solve problems and large-scale equation. Cylindrical coordinate system is used for the calculation of the discrete regions, so it can be very high computational efficiency in layer formation, borehole and equipment columnar model. Each discrete tetrahedral element gets four nodes and six edges. To improve the calculation speed and accuracy, we use the vector basis functions to simulate the electric field in each element of the distribution. Therefore, the effect of borehole and formation can be determined by finite difference time-domain (FDTD) method.The algorithm studied in this paper achieved good results in practice and can be used in the simulation of logging while drilling sensor response. It also can reach commercial levels, and have good value and prospects.