Study Of Numerical Simulation Of Triaxial Induction Logging In Planar-layered Anisotropic Medium

So far a great number of studies have confirmed that rocks in nature have various degrees of anisotropy.It is of great significance for oil exploration to fully understand the response characteristics of electromagnetic logging under the condition of electrical anisotropy.For example,sandstone and mudstonethin interbed which is a very important sedimentary reservoir has low horizontal resistivity and relatively high vertical resistivity and presents uniaxial anisotropy.Natural deposition and artificial pressure technology for petroleum production often cause fractures in oil and gas reservoirs.Fractures,as an important oil storage structure and seepage channel,will break the invariance of horizontal resistivity of uniaxial anisotropy medium and present biaxial anisotropy.In the high energy sedimentary environment,the inclined bedding is often formed,that is sandstone and mudstonethin interbed showing crossbeded anisotropy.When the fractures appear in the inclined bedding,full anisotropic stratum will be formed.Triaxial induction logging(multicomponent induction logging)tool and azimuthal electromagnetic wave logging tool based on the theory of triaxial induction logging are effective tools for detecting formation conductivity anisotropy.The simulation of the tool responses in logging environment is to solve electromagnetic field in inhomogeneity medium in mathematical model.The solution methods include numerical methods and analytical methods.Combined with the geological sedimentary and the effective detection range of the instruments,the logging environment can be simplified as a combination of horizontal layered model and a cylindrical layered model.Although the numerical algorithm has a strong applicability which can simulate complex instrument structure and logging environment at the same time,it needs a large workload and wastes a long time,which is inappropriate in the fast processing and iterative inversion of logging data.According to different analysis objectives,the influence of surrounding rocks and the borehole environment on instrument responses can be further separated,that is,independent research can be done on horizontal layered models or cylindrical layered models.Although these models are simple,they reflect the main contradiction of the logging problem.Analytical algorithm is usually used to simulate instrument response in layered structure model.The analytical algorithm has the advantages of fast calculation speed,high calculation accuracy,easiness to simplify the relationship between tool responses and model parameters and so on.It has a wide applicationin tool design,response simulation and characteristic analysis,fast processing of logging data and iterative inversion.In this paper,the anisotropic horizontal layered formation is studied.There have been a lot of works about the analytical algorithms of electromagnetic field in layered media including isotropy,uniaxial anisotropy and even biaxial anisotropy so far.However,there are few studies on total tensor anisotropy.In this work,the analytical solution of electromagnetic field in full anisotropic horizontal layered strata is derived systematically.The singularity of integrand function in numerical integration is solved.The responses and characteristics of triaxial induction instrument in full anisotropic formation are simulated and analyzed.In this paper,the electromagnetic field excited by magnetic/electric dipole sources in space domain is transformed into frequency wave number domain by two-dimensional Fourier transform.After eliminating the vertical components of electromagnetic field,a set of differential equations of horizontal components is obtained,which include a field vector,a system matrix and a source vector.By solving the eigenvalues and eigenvectors of the system matrix,the horizontal components of electromagnetic field are transformed into a mode-field containing upgoing and downgoing fields,and it is pointed out that the normalization of energy flow density of eigenvector of system matrix is not necessary.Next,in order to describe the propagation of mode fields in planar-stratified media,the concepts of generalized reflection and generalized transmission are introduced,the generalized reflection concept is used to solve the upgoing and downgoing wave coefficients in the source layer,and then the generalized transmission concept is used to solve the coefficients in other layers.By introducing the boundaries in the expression,the problem of numerical overflow is eliminated,which is convenient for programming.In addition,we make a profound study of the properties of electromagnetic field differential equations.In the published work,the field vector is composed of a specific sequence of four horizontal components of electromagnetic field.In this paper,it is extended to any sort form.The method has the advantages of clear physical image and concise derivation process.And then,the electromagnetic field in the space domain is obtained by the two-dimensional inverse Fourier transform.When the source and the field are in the xy-plane,the integrand is in the state of no convergence,which leads to the singularity problem.For the problem,the uniaxial background field is subtracted from the integrand function to eliminate non-convergence and accelerate the convergence of the solution.And then,the corresponding algebraic analytical solution of electromagnetic field in the space domain is added.This method not only solves the singularity problem of numerical integration,but also reduces the convergence region of the integrand,and prove calculation efficiency and stability.Finally,we simulate and study the influence of conductivityanisotropy,well deviation angle,azimuth angle,aye thickness and so on triaxial induction logging tool in full anisotropic formation.The theoretical derivation of electromagnetic field in full anisotropic formation is also applicable to the solution of electromagnetic field in biaxial anisotropic,uniaxial anisotropic and isotropic media.Besides electromagnetic wave logging,it is also applicable to other geophysical exploration research fields such as marine controllable source and airborne electromagnetic field.