Study On The Responses Of Azimuth Electromagnetic Wave Resistivity While Drilling By The Three-dimensional Finite Volume Algorithm Based On Electric Field Coupling Potential In Cylindrical Coordinate System

In the modern development of oil and gas exploration, logging while drilling(LWD) technology is often used in the drill collar to achieve real-time monitoring and geo-steering, which can effectively enhance the drilling success rate in the high-angle and horizontal wells, oil recovery efficiency and single well productivity. The principle of LWD tools is that the measurement devices, installed in the vicinity of the drill collar, can detect and save(or transmit to the ground) the layer information in real time while drilling in the layer. Because the mud has less influence on the new drilled layer, the measured results from the LWD tools can be closer to the real parameters of the layer. During the past thirty years, the LWD tools have include almost all the logging methods such as resistivity, sonic, neutron density, magnetic resonance, borehole imaging, et al. Using the compositive LWD technique, the LWD tools can not only achieve real-time geo-steering, but also comprehensively evaluate the complex oil and gas reservoirs. The azimuth electromagnetic wave resistivity while drilling tool is a new type of LWD tool, and it can solve the problem of the oil exploration in the anisotropic layers. The tool’s transmitting and receiving system consists of a series of inclined coils on the drill collar surface. Due to the drill II collar is rotating along while drilling, the electromagnetic field on different azimuths can be measured. The tensor type electromagnetic signals not only contain the layer information of the vertical and horizontal conductivity, relative layer dip and azimuth, but also contain layer boundary information. So the azimuth electromagnetic wave resistivity while drilling tool can meet the requirement of oils and gas evaluation and real-time geo-steering in complex reservoir better. In order to select the optimal instrument parameters(including coils spacing, operating frequency, the inclination angle of coil, etc.) and afford reliable and reasonable basis for the interpretation of LWD data, the corresponding 3D numerical modeling algorithm is urgent to be developed. According to the tool’s structure character, this paper will study the 3D numerical modeling algorithm suitable to the azimuth electromagnetic wave resistivity while drilling tool. The main contents are as follows:In the first chapter, we introduce the developing process of some main electric logging tools, the research background and significance of the azimuth electromagnetic wave resistivity while drilling. And then summarize the advantage and disadvantage of the modeling algorithms, such as analytic algorithm, NMM algorithm, FDTD algorithm, FE algorithm and so on. Finally, we outline the main research contents and innovations.In the second chapter, we will apply the finite volume algorithm in the cylindrical coordinates to establish the corresponding numerical method, so that we can effectively simulate the response of the tools in various complex environment and investigate the influence of the change in layers and tool parameters on the tool response. Therefore, according to the typical coil architecture of the instrument of azimuth electromagnetic wave resistivity while drilling, we firstly introduce the electrical and magnetic dyadic Green’s functions in inhomogeneous anisotropic layers by the electrical current source in the cylindrical coordinates. Through the superposition principle, we derive the integral formulation to compute the electric field intensity excited by tilted transmitter coils and to compute the induced electrical potential on tilted receiving coils both mounded on the drill collar. Then, we apply the coupled electrical potential of the dyadic Green’s functions to overcome the low inducing number problem during modeling the electrical field in inhomogeneous anisotropic layers. Furthermore, we use progressive grids in both ? and z directions to reduce number of grid nodes. On the basis, by applying three-dimensional finite volume method, we discrete the equations about the coupled electrical potential in the cylindrical coordinates and obtain the large sparse algebraic equation sets about the coupled electrical potential field on the Lebedev grid. The two methods of a combination of incomplete LU decomposition(ILUT) with the bi-conjugate gradient stabilization(BICGSATB) and pardiso are used to solve the numerical solution. Finally, we validate the algorithm by comparison of the numerical results obtained by two different methods, and study the impact of the drill collar, anisotropy, the tilted angles of both coil and borehole on the instrument response in inhomogeneous anisotropic layers.In the third chapter, two kinds of coils approximation methods, namely superposition electric dipoles and superposition magnetic dipoles, are discussed. The tool response under the two different approximation cases are compared. The results show that: whether the transmitter and receiver coils are tilted or not, the tool response under superposition electric dipoles has higher accuracy; only in the case of the transmitter(or receiver) keeping axial or the drill collar size being smaller, the tool response under superposition magnetic dipole has higher precision. So we can conclude: the superposition electric dipoles are more suitable to approximately model the transmitter coil in the azimuth electromagnetic wave resistivity while drilling tool.In the fourth chapter, by three-dimensional numerical simulation software established by the finite volume method in the cylindrical coordinates, we firstly investigate the tool response characters in vertical well and inclined well under the condition of fixed coils azimuth, and then study characters of the tool response affected by the coils azimuth.Under the condition of fixed coils azimuth: in the vertical well, when at least one of the transmitter or receiver coils is kept axial, the logging response is hardly affected by the mud; when both of the transmitter and receiver coils are kept tilted, the influence of mud on the tool response becomes obvious. Besides, at the vicinity of the boundary layer, the amplitude ratio and phase difference curves show significant horns effect due to the accumulation of surface charge. In the inclined well, with the increase of the inclined angle, the tool response is more affected by the mud, whether the coils are axial or tilted. Three coil system in logging will result in the overall migration log response, four coils have a symmetrical coil architecture, eliminating the offset of the log response. Therefore, logging four coil system responding to the position reflects the boundary layer more accurately.Under the condition of continuous coil azimuth change: in the uniform anisotropic layer, the amplitude ratio and phase difference change with azimuth are bilaterally symmetric at 180 degree. When the inclined angle increases, the tool response is more affected by the azimuth. One of the function of the azimuth electromagnetic wave resistivity while drilling tool has strong detecting ability of boundary layers, which can be used in geo-steer. In order to compare the boundary detecting ability of the tools with different structures, we let the tools pass through the symmetry layer model, and investigate the tool’s response characters on the boundary. The 3D figures of phase difference and amplitude ratio with different depth and different azimuths show: the responses of the tool with single transmitter coil behave differently at the positions of the tool entering and leaving, the whole phase difference and amplitude ratios are also asymmetric even in the symmetric layer model, which is caused by the shift of the coils. However, the response of the tool adopting symmetric double transmitter coils is almost symmetric, regardless of the phase difference or the amplitude ratio. Besides, when the operating frequency decreases, the amplitude ratio and phase difference are both become small, relatively. This testifies that the influence of the azimuth on the tool response will be greater if the tool’s frequency is higher. Compared to the tool with tilted coils, the tool with coplanar coils is sensitive to the bed boundary, which prove the tool to have stronger boundary detecting ability.