Forward And Inversion Of Electromagnetic Wave Logging While Drilling Of VTI And TTI Medium In Highly Deviated/Horizontal Wells

During the process of petroleum exploration and development,high-angle wells/horizontal wells have been widely used because of their unique technical advantages.Logging while drilling resistivity mesurment is an important method to obtain these kind of resistivity logging data.Based on LWD resistivity logging inversion,formation resistivities and interfaces can be reconstructed accurately.Then the reservoir evaluation and geological steering ability in highly deviated wells / horizontal wells can be effectively improved.We use traditional LWD electromagnetic and multi-component induction logging as examples.Based on the relalistic formation sedimentary environment,the forward and inverse numerical simulation of different geological conditions(VTI and TTI strata)has been carried out systematically,which overcomes the limitations of the current VTI stratum model in the actual application.This would make up the deficiency of domestic research in this field.The relative characteristics of LWD resistivity responses in TTI formation with staggered bedding under different formation conditions are analyzed in detail,which provides a theoretical basis for qualitative logging interpretation;sensitivities of well deviation,anisotropic angle,anisotropic azimuth and formation resistivity are studied,providing the solid theoretical basis for the qualitative interpretation in complicated formation conditions and the development of related new logging instruments.We also establish the fast inversion theory and algorithm for complex stratum structure and optimize the sliding inversion window design scheme,and propose the idea and strategy of constrained optimization for inversion initial value by using adjacent well logging,regional geological and seismic data are proposed.A novel Huber inversion algorithm is proposed to solve the problem that the traditional inversion algorithm is only suitable for logging data with Gaussian noise,which makes the inversion more robust and more applicable.The whole set of forward and inverse theories and algorithms proposed in this paper can be used for reservoir evaluation and geological steering in high-angle wells/horizontal wells under complex geological conditions.It can be used for any commercial induction logging tool.In Chapter 2,the forward numerical algorithms of LWD electromagnetic wave and multicomponent induction logging under differet sendimental enviorments are deduced in detail.We also introduce the corresponding electromagnetic field integration methods.Firstly,the expression of electromagnetic field in VTI media based on Hertz potential function is given,and the method of calculating electromagnetic field in multi-layered VTI media is deduced by using propagation coefficient matrix and generalized reflection coefficient.Then,for TTI stratigraphic model with interbedding,the general solution of electromagnetic field in infinite medium is derived in detail based on dyadic Green's function.Using the half-space medium,the half reflection and transmission matrices are defined,and then the generalized reflection and transmission matrices in multi-layered medium are obtained;the direct and scattering fields in TTI medium with staggered layers are given in detail;the total electric field at the receiving coil under different conditions is summarized;solving the electromagnetic field integral expression by numerical methods of Gauss integral and Hankel integral.In Chapter 3,we present the LWD electromagnetic and multi-component induction logging responses in VTI medium and in TTI medium.We also give the corresponding sensitivity analysis.Specifically,firstly,half space reflection and transmission characteristics of electromagnetic wave in VTI medium and TTI medium are compared and analyzed.Then we discuss the limitations of Hertz potential function and generalized reflection coefficient method.The LWD electromagnetic and multi-component induction logging response with different well deviation,azimuth,anisotropic angle,anisotropic azimuth and stratum thickness are systematically summarized,and the concepts of critical anisotropic angle and critical well deviation angle are proposed in the very first time.Finally,the sensitivity of well deflection,azimuth anisotropy angle,anisotropy azimuth and formation resistivity is studied.In Chapter 4,we introduce the inversion theories and algorithms of resistivity logging while drilling in highly deviated wells and horizontal wells.Firstly,we review the borehole dip,shoulder/thickness and anisotropy correction method by using corresponding charts and show how to implement the chart correction method in detail.Also we list the advantages and disadvantages of chart inversion method.The least squares inversion theory based on L2 norm is analyzed,and the inversion objective function is established.We introduce the algorithms of Gauss Newton and Levenberg Marquette to solving the least squares problem.Then we propose the Huber norm inversion theory and estblisth its objective function based on L2 and L1 norms.We slove this kind of inversion method by using Gaussian Newton method.Based on the traditional sliding window design,a new sliding inversion window scheme is given,which guarantees the global optimum of inversion results and takes into account the calculation speed.To solve the problem that inversion is easy to fall into local optimum,a multi-initial value method is given first.Also,introducing some multi-initial value optimization strategies.Several global stochastic intelligent optimization algorithm theories and correspongding implementation are introduced.They are based on a random set of initial values,and then continue to search for the optimal solution.In Chapter 5,we show the implementation procedures and numerical examples of logging while drilling electromagnetic wave inversion in highly deviated and horizontal wells.Firstly,the formation model should match the actual formation and the corresponding forward algorithm should be selected,when the actual logging,regional geology and seismic data are obtained.Secondly,the more inversion parameters computated,the more local optimal solutions would be obtained.More inversion parameters would also influence the calculation speed and accuracy.Therefore,it is proposed that the appropriate inversion target parameters should be selected according to the truly demand(geological guidance or fine logging interpretation).The strategy of selecting input logging data and the criterion of termination condition of inversion iteration are given,and the influence of well deviation angle,stratum interface position and stratum model on inversion effect is analyzed.The anti-noise performance of LS algorithm and Huber algorithm to Gaussian noise,non-Gaussian noise and mixed noise are investigated respectively.It is pointed out that Huber inversion is more stable and applicable than LS inversion.Finally,a synthetic example based on the actual formation model is established to verify the related algorithms involved in this paper.