Study On The Iterative Regularization Inversion Of Dual Laterolog Datum And The Numerical Simulation Of Multicomponent Induction Logging Responses In General Anisotropic Formations

The work of this paper can be divided into two parts: in the first part, according to the difficulty of interpretation and evaluation about thin reservoirs and thin interactive reservoirs in current Daqing oil field, whose thickness of individual laminate is smaller than 1 m, we present a iterative regularization algorithm to simultaneously reconstruct all the model parameters, including the virgin formation resistivity, flushed zone resistivity, invasion radius, horizontal boundary depth and mud resistivity per bed, from dual-laterolog (DLL) datum based on nonlinear inversion theory and Morozov discrepancy principle. In the second part, we present an efficient algorithm to numerically simulate the responses of multi-component induction logging (MCIL) tool in layered anisotropic formations by using propagator matrix method (PMM) for investigating the response characteristics of MCIL tool in layered general anisotropic formations, which can become a theoretical basis of new instrument design and data processing.The electrical logging is one of the most basic and important logging method in petroleum logging. It can classify the lithology, estimate the hydrocarbon saturation and predict the oil-gas production capacity by detecting formation resistivity. The DLL tool is the most widely used logging tool in current domestic, in practical application it usually combined with microspherically focused logging (MSFL) tool to determine the position of permeability formation and identificate the oil-water bed. How to fast and efficiently simulate the logging response in complex formations has important significance to logging data interpretation and inversion algorithm establishment. In chapter 2, a fast forward algorithm for DLL in layered inhomogeneous medium has been set up. The fast algorithm and the semi-analytical expression of Green's function in layered inhomogeneous formations have been given by numerical mode matching method (NMM) firstly. Then the integral equations on potential values and current distributions of beam electrode, shielding electrodes and monitor electrodes have been established by considering the special structure of DLL tool. Finally, we combine the integral equations with focusing conditions to calculate the logging responses of deep and shallow lateral. Besides, the differences in detecting depth and vertical resolution between dual induction logging tool (DIT) and DLL tool are investigated by geometric factor theory. The numerical results show that the DIT has deeper detecting depth than the DLL tool, and the vertical resolution of DLL tool is much higher than the DIT's.With the development of oil field, people find the logging response values in thin reservoirs and thin interactive reservoirs cannot completely, even incorrectly, reflect the formation parameter information because of the influence of complex environment around the borehole and the self-limiting of instrument. So the inversion processing of well-logging datum is necessary. The inversion of well-logging datum is a mathematically representative ill-posed problem for the nonuniqueness and instability. In order to improve the reliability of inversion results, we present a new iterative regularization inversion algorithm in chapter 3. First, the Born's approximate formulae of DLL responses and the relation between perturbations of formation conductivity and small changes of model vector are given by perturbation principle. In combination with the forward modeling method, a fast algorithm of normalized Fréchet derivative matrix has been set up. Then a stabilizing function is introduced, which is a non-quadratic function including the derivative of electric conductivity and invasion radius. From the Tikhonov regularization inversion theory, the inversion problem can be transformed into the minimization problem of non-quadratic objective function with the stabilizing functional defined on model space. The minimization of objective function can be obtained by using Gauss-Newton method. In the iterative process, the combination of Morozov discrepancy principle and Cholesky decomposition is executed to propose an a-posteriori regularization factor choice strategy in order to obtain a stable and reliable inversion solution. Thus, not only the objective function and the fitting error of well-logging responses decreased continually, but also the best fit of input data with modeling logs has been realized. The numerical results of theoretical models show that the full-parameter iterative regularization inversion technique can not only reconstruct the real values of virgin formation resistivity and flushed zone resistivity effectively, but also improve the stability and reliability of inversion solutions. It is necessary to make the mud resistivity as a independent inversion parameter when inversing DLL datum, because the detecting depth of DLL tool is more shallow and its response is more sensitive to the changes of mud resistivity than DIT's. The inversion results of field logs measured from Daqing oil field show that the inversion results of DIT and DLL datum accord with the test oil conclusion at many test oil layers, but the inversion effect of DLL datum are much better than DIT's in thin reservoirs and thin interactive reservoirs, whose thickness of individual laminate is smaller than 1 m, and it has very important significance to inverse DLL datum in thin reservoirs identification and classification.The electric anisotropy phenomenon hadn't aroused attention to people in early stage of electrical prospecting. With the constrant progress of drilling and logging technology, the study on response characteristics of logging tool in anisotropic formations and influence of formation anisotropy to instrument measure have been gradually concerned by people. The multi-component induction logging (MCIL) is a newly logging technology which can simultaneously measure the formation conductivity with different directions in anisotropic formations. The study on simulation and inversion of logging response under different formation conditions is a very important research topic in current petroleum logging. The forward study in stratified medium is mostly assumed the formation is transverse isotropy (TI), there is no report about the numeirical simulation of MICL responses in layered general anisotropic formations now. In chapter 4, an efficient algorithm to numerically simulate the responses of MCIL in layered anisotropic formations by using propagator matrix method. First, the solving problem of Maxwell's equations in frequency-spatial domain is transformed into a definite solution problem of first-order ordinary differential systems in frequency-wavenumber domain by Fourier transform. The electromagnetic (EM) field can be decomposed into upgoing and downgoing mode by using eigenvalues and normalized eigenvectors of the system matrix. And an analytical expression of electromagnetic wave emitted by an arbitrary direction of magnetic dipole in homogeneous anisotropic media is derived. Then we derive the recurrence formula of generalized reflection coefficient per interface and that of amplitude of electromagnetic wave each bed by studying the reflection and transmission of electromagnetic wave in layered anisotropic formations based on superposition principle and interface conditions. By this method, it can avoid computing lots of matrices multiple directly. In order to determine numerical solution of electromagnetic field in frequency-spatial domain, a 2D adaptive Patterson integral formula and the limitedly continued fraction expansion technique are used to compute the 2D inverse Fourier transform, which can improve the operation efficiency and the calculation accuracy. Finally, the numerical tests validate the new algorithm and investigate the response characteristics of MCIL tool in layered orthorhombic anisotropic formations: the variations of horizontal anisotropy coefficient can not change the logging response of Y axis, the variations of vertical anisotropy coefficient can not change the logging response of Z axis, the growth of tool length can lead to the vertical resolution reduction, the increase of work frequency can cause much higher skin effect, the changes in borehole dipping angles can not only affect the logging responses in three principle axes direction but also generate counter responses of X axis and Z axis.