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A robust and succinct matrix-based method is developed to simulate the response of eccentered resistivity logging tools in anisotropic geological formations. This is done by first deriving the solution of the state vector describing the potential and the current component along the radial direction in a cylindrical system. Rescaled cylindrical eigenfunctions are employed to overcome the poor scaling inherent to the canonical cylindrical functions for very small or very large arguments. A Levin-type method for approximating integrals with rapidly oscillatory functions is introduced to effectively perform the numerical integrals. The influence of both the translational and rotational eccentricities of the logging tool within the borehole surrounded by an anisotropic formation is studied based on numerical results provided by the present matrix method. We found that neither translational nor rotational eccentricity can be neglected, especially in low-resistive or anisotropic geological formations. [ABSTRACT FROM AUTHOR]

A robust formulation is presented to eliminate overflow, underflow, and convergence problems that arise the computation of tensor Green’s functions in cylindrical multilayered media under finite-precision arithmetic. This is done by first introducing a set of rescaled functions associated to the (canonical) cylindrical Bessel and Hankel functions representing standing waves and outgoing waves along the radial direction. The rescaled cylindrical functions are designed to avoid the poor scaling inherent to the canonical cylindrical functions for very small or very large arguments. In addition, a parabolic Sommerfeld integration path is constructed in the spectral complex plane to yield a numerical integration with good convergence properties for a wide range of parameter values. [ABSTRACT FROM PUBLISHER]

A high-frequency electromagnetic-wave logging (HFEL) tool has been developed to detect the dielectric constant and resistivity of the sedimentary formation by measuring the phase difference and amplitude ratio synchronously. The single-parameter deconvolution method is a convenient tool for enhancing the vertical resolution of the curves and reshaping the curves themselves. This paper attempts to resolve the two parameters, the dielectric constant and the resistivity, which are employed in the deconvolution method from two responses: the phase difference and amplitude ratio. First, an adaptive dual-parameter deconvolution method for the HFEL dielectric constant and resistivity measurements is devised to enhance the vertical resolution of the tool and to more accurately extract the formation parameters, namely, the dielectric constant and resistivity. The advantages of this method are revealed in the numerical experiments on the synthetic and actual logging data. The adaptive dual-parameter deconvolution can be informative in the application of the deconvolution. [ABSTRACT FROM AUTHOR]

From the actual development and testing requirements of horizontal wells in domestic oilfields, according to the problems that the common sensors have relatively low resolution during the water cut measurement for the oil–water flow in the horizontal wells with medium and low production, a trielectrode capacitance sensor (TECS) is designed and a water cut measurement system based on TECS is developed for different conditions of horizontal oil–water flow. Specifically, the electrostatic field distribution of the annular measurement region is investigated under different conditions of horizontal stratified flow. Then, its equivalent capacitance on the electrodes is analyzed. Based on the simulated results, the effects of structural parameters on sensitivity distribution are analyzed, including the electrode length, the radius of the flow channel, and the thickness of the insulation, determining its optimal structure. Moreover, the static and dynamic experiments, as well as the field testing, validate the designed TECS, indicating that the TECS enables measuring the water cut of horizontal oil–water flow, especially under low flow rate and oil–water stratified conditions. The developed TECS could realize the water cut measurement with a wide flow rate range (3–60 m $^3$ /d) and the full water cut range (0%–100%) for the horizontal oil–water flow. [ABSTRACT FROM AUTHOR]