Gong Li Wang

Two-Dimensional inversion of triaxial induction logging data in transversely isotropic formation

In this paper, we present a two-dimensional inversion method for triaxial induction logging data in a layered and transversely isotropic formation with invasion. With a triaxial transmitter and receiver, all nine components of the apparent resistivity tensor can be measured, making it possible to invert for the resistivity in the vertical direction. We choose the Gauss-Newton method as the inversion engine and use the multiplicative regularization method to determine the damping coefficient automatically. Different line search methods are studied, and their influences on the convergence are discussed. Two synthetic examples are presented to demonstrate the capability and performance of the inversion algorithm.

Two-dimensional inversion of triaxial induction logging data using a fast forward solver

Summary form only given. The tensor type data acquired by the triaxial induction tool enables the determination of not only resistivity, but also resistivity anisotropy of reservoir. The most popular anisotropic model for triaxial data interpretation is a horizontally layered formation with transversely isotropic (TI) resistivity anisotropy in each bed. When there is invasion developed in a permeable reservoir, the invasion effect can be so strong that including invasion in the forward model becomes mandatory in order to obtain reliable resistivity estimation. In this paper, we present an inversion method that is able to take the invasion effect into account. The inversion is based on the Gauss-Newton approach with the L2-norm regularization technique that not only ensure the stability of the inversion, but also greatly enhances the resolution of reconstructed model in thinly-layered formations. The formation model that we use in the inversion is a multilayer model in which the invasion, e.g., the simple step-profile invasion, or the annulus invasion, can be modeled in each bed. Due to the presence of invasion, the problem is not 1D anymore. A high efficient forward solver is developed that can accurately and rapidly model the response of the triaxial induction tool to both bed boundary and invasion in multilayer formations. The new method solves for all three electric field components numerically with a hybrid method in the cylindrical coordinate system assuming the formation is axially symmetric. Numerical experiments show that the hybrid method works well for a frequency down to kHz range for induction logging tools. The new method is up to two orders of magnitude faster than existing 2D finite-difference forward solvers. Such a high speed guarantees the 2D inversion can be run in a commonly-used desktop computer within a reasonable timeframe. The richness of the triaxial induction data makes the inversion work fairly well in various situations. Numerical experiments on synthetic data demonstrate that the inversion is able to reliably correct for the invasion effect, and find the right anisotropic resistivity in the virgin zone of invaded beds. The capability is from the addition of co-planar measurements together with multiple spacings to provide the sensitivity to anisotropy and significantly improve the data sensitivity to resistivity change in the radial direction.

Electromagnetic modeling and inversion application for oil and gas industry

An essential objective of collecting measurements in the oil and gas industry is to detect, locate and quantify the amount of oil and gas in the Earth subsurface. Electromagnetic measurements either at DC, induction, propagation, and dielectric frequencies play a central role because electromagnetic properties of hydrocarbon and water are very different. These electromagnetic measurements can be collected either from a single borehole (e.g., laterolog, induction logging, electromagnetic geosteering, and dielectric logging), multi-boreholes (e.g., cross-well electromagnetic, surface-to-borehole electromagnetic), or at surface (e.g., magnetotelluric, controlled-source electromagnetic). The process to convert electromagnetic measurements into electromagnetic property (e.g., resistivity/conductivity and permittivity) map of the subsurface is an ill-posed problem. Furthermore, due to the substantial differences in electromagnetic properties of Earth subsurface especially hydrocarbon and water, the inverse problem can only be properly solved using a full nonlinear inversion algorithm. In addition the number of data points can be very limited, hence making the ill-posed problem more severe.

Using a contraction mapping method to determine complex permittivity from electromagnetic propagation measurements

In typical logging while drilling propagation-resistivity tools, formation properties are measured at different operating frequencies. The conductivity and permittivity of the formation are obtained from the inversion of the measured amplitude attenuation and phase shift between a pair of receiver antennas. This paper describes a simple method for computing formation resistivity and permittivity from electromagnetic propagation measurements. It starts with a closed-form solution for a generic propagation tool in homogeneous and isotropic media and uses a contraction mapping method for inverting conductivity and permittivity.

Inversion for tilted triaxial conductivity in dipping layered formations

In this paper, a one-dimensional inversion method is presented to determine tilted triaxial conductivity in a dipping layered formation using triaxial induction measurements. The tilted triaxial conductivity is described by three conductivity components and three Euler angles. The inversion problem is solved with the Gauss-Newton method combined with the multiplicative regularization technique. There are six principal coordinate systems that can give the same conductivity tensor. Permutation is performed to eliminate the ambiguity of inversion results caused by the ambiguity of the principal coordinate system. Three new Euler angles after permutation for each layer can be found by solving a nonlinear equation.