Efficient finite-volume simulation of the LWD orthogonal azimuth electromagnetic response in a three-dimensional anisotropic formation using potentials on cylindrical meshes

In this study,the cylindrical finite-volume method(FVM)is advanced for the efficient and high-precision simulation of the logging while drilling(LWD)orthogonal azimuth electromagnetic tool(OAEMT)response in a three-dimensional(3 D)anisotropic formation.To overcome the ill-condition and convergence problems arising from the low induction number,Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system.The electrical fi eld continuation method is applied to approximate the perfectly electrical conducting(PEC)boundary condition,to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels.On the base,the 3 D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries.The equivalent conductivity in a non-uniform element is determined by a standardization technique.The direct solver,PARDISO,is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem.To reduce the number of calls to PARDISO,the whole computational domain is divided into small windows that contain multiple measuring points.The electromagnetic(EM)solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix,relevant to all the transmitters in the same window,is changed.Finally,the 3 D FVM is validated against the numerical mode matching method(NMM),and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

Numerical and physical simulations of array laterolog in deviated anisotropic formation

Due to the tremendous amount of high-resolution measurement information,array laterolog is widely used in evaluations of deviated anisotropic reservoirs.However,the precision of a complementary numerical simulation should be improved as high as the core of fine-scale reservoir evaluation.Therefore,the 3D finite element method(3D-FEM)is presented to simulate the array laterolog responses.Notably,a downscaled physical simulation system is introduced to validate and calibrate the precision of the 3D-FEM.First,the size of the downscaled system is determined by COMSOL.Then,the surrounding and investigated beds are represented by a sodium chloride solution and planks soaked in solution,respectively.Finally,a half-space measurement scheme is presented to improve the experimental efficiency.Moreover,the corresponding sensitivity function and separation factor are established to analyze the effects of the formation anisotro py and dipping angle on the array laterolog responses.The numerical and experimental results indicate that the half-space method is practical,and the mean relative error between the numerical and experimental results is less than 5%,which indicates that the numerical simulation is accurate.With the proposed approach,the reversal angle of array laterolog response curves in anisotropic formations can be observed,and this range is determined to be 50°-62°.