Numerical Simulation Of Dielectric Logging Based On The Method Of FEM-DDM

Even though the high speed development of science and technology,it haven’t even reduced a litthe the dependence to the human beings on oil.Besides,the demand for oil is increasing in modern industry and the oil exploitation is becoming more and more difficult.In the petroleum exploration project, the requirement of the detecting ability of well logging instrument is more and more high.The dielectric logging tools,which has received increasingly attention,is a powerful supplement to the traditional well logging methods.It will be ueed and play an important role When the resistivity of the formation is not changed obviously,or under the condition of unknown resistivity.In this paper, we first introduce the dielectric logging theory, from the strata of the dielectric properties, mechanism of polarization and dispersion effect,discuss the principles of electromagnetism which can be used to distinguish the formations.Then,we analisis the forward modeling and inversion modeling methods under homogeneous and inhomogeneous formations.For forward modeling analysis,in homogeneous formations and different frequencies,the improved plane wave model and the spherical wave model can be ueed to compute different analytic solutions.Although the analytical solution can not be directly used to explain the real situation,it also play a important role in theverification and guidance for the simulation modeling.And to the modeling of real situation of inhomogeneous formation, we use the method combination with tne finite element method with the domain decomposition method(FEM-DDM) to modele and analysis.The finite element method can simulate the irregular model well.The domain decomposition method can divide the whole domain into several sub regions.Comprehensive above,the FEM-DDM methodcan greatly reduces the number of unknown quantities under the premise of ensuring the accuracy.In the paper,we discuss the frequency point, source distance, detecting depth, resolution, applicability of the Dielectric Logging Method.For inversion modeling analysis,the application of improved plane wave model and spherical wave model are also discussed in homogeneous formations.Then the numerical inversion algorithm is analyzed.Under the premise of the approximate algorithm, the objective function is easy to be ill conditioning in the iterative process, which leads to the divergence of the iteration,and leads to the failure analysis.This paper proposed improvement method which is adding the appropriate regularization methods in the objective function and each step of the iteration process the objective function will be corrected.Also under the FEM-DDM framework,combining the Newton iteration with the regularization method, the inversion analysis will be carried out on the model of dielectric logging.Using the FEM method,The sensitivity matrix will be filling only one step.Using the domain decomposition algorithm,the inversion analysis can be computed in parallel.Combining above,solving efficiency will be greatly improved.The numerical results mentioned in this paper are in good agreement with the measured values or literature results,fully proged the accuracy of the method used in this paper.The analysis in this paper provides a reference for the related research theory of dielectric logging, which lays a foundation for further research.