Study Of Numerical Simulation And Characteristics Of Multi-component Induction Logging Response In Anisotropic Media

In current geophysical well logging, it is very important to study responses of multi-component induction logging tool (MCIL) in anisotropic formation by numerical modeling techniques. Through the numerical modeling, we can systematically investigate responses of MCIL in various complex formations so that we can choose appropriate tool parameters during design of tool and establish efficient algorithm of data processing and inversion to pick out useful signals from the measurement. In the paper, it has been systematically studied three main problems including analytical expressions of dyadic Green function in a homogeneously anisotropic formation, the numerical modeling of responses of MCIL in cylindrically layered anisotropic formation and extension of geometric factor theories from traditional induction to MCIL, and some useful theoretical and applicable achievement has been obtained. Concrete contents are following.In chapter one, it mainly summarizes the significance and current development status of MCIL. Chief research contents and methods are also summed up in the paper.In chapter two, Fourier transformation and decomposition of TE and TM waves are used to try to establish the analytic algorithm of electromagnetic dyadic Green functions in a homogeneous anisotropic media. Through Bessel integral formulae, the analytic expressions of both electric and magnetic dyadic Green functions by electric and magnetic sources are obtained.In chapter three, basing on perturbation theory, geometric factors in conventional induction logging have been extended to explore responses of MCIL in anisotropic formation. Through the relationship of small perturbation of conductivity to magnetic dyadic Green functions by magnetic sources and Born approximate, we establish the formulae of differential geometry factors of MCIL to study spatial responses of different components of MCIL so that we can efficiently investigate response characters of both coaxial and coplanar coil systems and their difference. The numerical results show concretely spatial sensitivities of the three principal components (σ_a,xxσ_a,yyσ_a,zz) to spatial changes in horizontalelectrical conductivity and vertical conductivity. Then, we further apply integrals of the spatial responses in radial and vertical directions respectively to define vertical and radial differential geometry factors of MCIL so that we can conveniently explore vertical resolution and radial investigation depth of MCIL in various environments. The integrals in both radial and vertical directions are obtained by adaptive Simpson quadrature. It has given many numerical results of the vertical and radial differential geometry factors for different conditions such as changes in anisotropic coefficients and tool length etc. Through a lot of numerical tests, we have gotten the following conclusions about the responses of MCIL: The spatial responses of coplanar system are entirely different from that of coaxial system. The former is greatly sensitive to change in both horizontal and vertical resistivities while the later is only responsible to change in horizontal resistivity. In addition, the spatial response of coplanar system is strongly influenced by anisotropic coefficient as well.Chapter IV, we use mixed potential theory and advance an algorithm to solve Maxwell's equation in cylindrically stratified anisotropic media. First, we use Fourier transformation to extract TE and TM waves from Maxwell's equation, and derive their corresponding equations and the relationship between horizontal and vertical components of EM field. Then basing on continuous conditions of EM field on interfaces, we establish formulae of reflection,transmission coefficient,generalized reflection coefficients on every boundary and the amplitude's recursive of EM fields on the adjacent beds. Finally we develop Fortran code to compute EM field produced by magnetic dipole located any position field in order to accurately calculate the response characteristics of MCIL in the cylindrically stratified anisotropic media and systematically investigate the influence of the change in apparatus eccentric,formation resistivity and borehole mud etc. on logging responses.The results clearly show that unlike the coaxial coil system, the responses of coplanar coil systems are strongly nonlinear, their measurements are highly sensitive to changes in mud resistivity,tool length,eccentric,invasion radius and anisotropy coefficient, and the negative responses often appear. In order to extract reliable vertical resistivity from the measurement of MCIL, some new and complex inversion techniques will be needed to develop.