2.5-Dimensional modeling of EM logging-while-drilling tool in anisotropic medium on a Lebedev grid

A 2.5D finite-difference(FD)algorithm for the modeling of the electromagnetic(EM)logging-whiledrilling(LWD)tool in anisotropic media is presented.The FD algorithm is based on the Lebedev grid,which allows for the discretization of the frequency-domain Maxwell's equations in the anisotropic media in 2.5D scenarios without interpolation.This leads to a system of linear equations that is solved using the multifrontal direct solver which enables the simulation of multi-sources at nearly the cost of simulating a single source for each frequency.In addition,near-optimal quadrature derived from an optimized integration path in the complex plane is employed to implement the fast inverse Fourier Transform(IFT).The algorithm is then validated by both analytic and 3D solutions.Numerical results show that two Lebedev subgrid sets are sufficient for TI medium,which is common in geosteering environments.The number of quadrature points is greatly reduced by using the near-optimal quadrature method.

Real-time forward modeling and inversion of logging-while-drilling electromagnetic measurements in horizontal wells

Based on the pseudo-analytical equation of electromagnetic log for layered formation,an optimal boundary match method is proposed to adaptively truncate the encountered formation structures.An efficient integral method is put forward to significantly accelerate the convergence of Sommerfeld integral.By asymptotically approximating and subtracting the first reflection/transmission waves from the scattered field,the new Sommerfeld integral method has addressed difficulties encountered by the traditional digital filtering method,such as low computational precision and limited operating range,and realized the acceleration of the computation speed of logging-while-drilling electromagnetic measurements(LWD EM).By making use of the priori information from the offset/pilot wells and interactively adjusting the formation model,the optimum initial guesses of the inversion model is determined in order to predict the nearby formation boundaries.The gradient optimization algorithm is developed and an interactive inversion system for the LWD EM data from the horizontal wells is established.The inverted results of field data demonstrated that the real-time interactive inversion method is capable of providing the accurate boundaries of layers around the wellbore from the LWD EM,and it will benefit the wellbore trajectory optimization and reservoir interpretation.

Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

A novel,highly efficient and accurate adaptive higher-order finite element method(hp-FEM)is used to simulate a multi-frequency resistivity loggingwhile-drilling(LWD)tool response in a borehole environment.Presented in this study are the vector expression of Maxwell’s equations,three kinds of boundary conditions,stability weak formulation of Maxwell’s equations,and automatic hpadaptivity strategy.The new hp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation.Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom,which provides more accurate results than those obtained using the adaptive h-FEM.The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models,which further confirm the accuracy of the results using the Hermes library(http://hpfem.org/hermes)with a multi-frequency resistivity LWD tool response in a borehole environment.

Fast anisotropic resistivities inversion of loggingwhile-drilling resistivity measurements in highangle and horizontal wells

Information about anisotropic resistivity is essential in real-time correlation,updating of formation model and making more confi dent geosteering decisions in logging-while-drilling(LWD)application.However,abnormal responses such as curve separations and apparent resistivity“horns”often exist in the LWD resistivity measurements due to the infl uences of complex downhole environments.Thus,accurate formation resistivity is not readily available.In this paper,we present an effi cient inversion scheme for the rapid estimation of anisotropic resistivity from LWD resistivity measurements acquired in high-angle and horizontal wells.Several strategies are adopted in the inversion:(1)a one-dimensional(1D)simulator with a simplifi ed three-layered model guarantees the forward speed and keeps the number of inverted parameters as few as possible;(2)combined with geological and petrophysical bounds,the tool constraints derived from a detection capability analysis of LWD resistivity measurements are applied to scale down the inverted parameters’searching scope,which avoids meaningless solutions and accelerates the inversion signifi cantly;(3)multiple-initial guesses are used in the inversion to ensure a global solution.Inversion results over synthetic examples demonstrate that the proposed 1D inversion algorithm is well suited for complex formation structures.It is also robust and fast in extracting anisotropic resistivities from LWD resistivity measurements.

A new deep-reading look-ahead method in electromagnetic loggingwhile-drilling using the scattered electric field from magnetic dipole antennas

This paper presents a new deep-reading logging-while-drilling electromagnetic(EM)logging method to detect bed boundaries ahead of bit.Unlike all existing EM logging approaches,the new method is based on the scattered electric field radiated by a magnetic dipole antenna.By analyzing the characteristics of electric tensor responses in layered formations,optimal look-ahead electric component is selected.The selected scattered field contributes to a large portion of the total field and is strongly sensitive to the boundary position.The measured voltage from the scattered electric component can be tens of times larger than that from the scattered magnetic fields and it attenuates slower.Thus,the detection capability improves significantly.A coaxial open-loop half-circle antenna is then proposed to measure the electric field in logging while drilling environment.A practical tool implementation equipped with two tilted close-loop antennas and two open-loop antennas is further developed for look-ahead application.Numerical results demonstrate that the detection depth of the new look-ahead tool can be up to 40 m under favorable conditions.Compared with current look-ahead logging tools,the new method not only significantly shortens the tool size,but also can recognize the boundary position and azimuth.