Extra-deep Azimuthal Resistivity Research Articles

Algorithm for inversion of resistivity logging-while-drilling data in 2D pixel-based model

Multi-frequency and multi-component extra-deep azimuthal resistivity measurements with depth of investigation of a few tens of meters provide advanced possibilities for mapping of complex reservoir structures. Inversion of the induction measurements set becomes an important technical problem. We present a regularized Levenberg–Marquardt algorithm for inversion of resistivity measurements in a 2D environment model with pixel-based resistivity distribution. The cornerstone of the approach is an efficient parallel algorithm for computation of resistivity tool signals and its derivatives with respect to the pixel conductivities using volume integral equation method. Numerical tests of the suggested approach demonstrate its feasibility for near real time inversion.

LWD DATA INVERSION FOR STRUCTURE WITH ANGULAR UNCONFORMITY

Non-structural traps and reservoir flanks are characterized by angular unconformities. Angular unconformity between dipping formation and sub-horizontal oil-water contact is common in the North Sea fields. This paper presents an approach to real-time inversion of LWD resistivity data for the scenario with angular unconformity. The approach utilizes artificial neural networks (ANNs) for calculating the tool responses in parametric surface-based 2D resistivity models. We propose a parametric model with two non-parallel boundaries suitable for scenarios with angular unconformity and pinch-out. Training of ANNs for this parametric model is performed using a database containing samples with the model parameters and corresponding tool responses. ANNs are the kernel of 2D inversion based on the Levenberg-Marquardt optimization method. To demonstrate applicability of our approach and compare with the results of 1D inversion, we analyze Extra Deep Azimuthal Resistivity tool responses in a 2D synthetic model. It is shown that 1D inversion determines either the position of the oil-water contact or dipping layers structure. At the same time, 2D inversion makes it possible to correctly reconstruct the positions of non-parallel boundaries. Performance of 2D inversion based on ANNs is suitable for real-time applications.

Numerical solution of the integral equations of the electromagnetic field in geosteering problems

Extra-deep azimuthal resistivity measurements improve the depth of investigation up to 30 m from the wellbore. Interpretation of electromagnetic logging data in the neighbourhood of a well becomes an important technical problem. We present an efficient parallel method for computation of induction tool responses with multiple transmitter–receiver configurations in 2D pixel-based anisotropic model crossed by an arbitrary well trajectory. The cornerstone of the approach is volume integral equation method. We consider the conductivity distribution as a sum of background and anomalous conductivities. Background conductivity is 1D-layered. Anomalous conductivity has arbitrary 2D distribution. Electromagnetic fields are the superposition of background and anomalous fields. Background fields are calculated exactly using rigorous analytical solution for 1D-layered background model. With this approach, the 2D pixel-based model is treated as an extension of the 1D-layered model. The anomalous fields are required only in pixels with conductivity different from the conductivity of the 1D-layered model. Anomalous fields are calculated using convergent series of integral operators [1]. The approach takes into account conductivity anisotropy and allows obtaining both the exact solution and the fast approximate one. The convergence of approximate solution is investigated on some synthetic examples.

Calculation of Tilted Coil Voltage in Cylindrically Multilayered Medium for Well-Logging Applications

In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR).

Detection performance and inversion processing of logging-while-drilling extra-deep azimuthal resistivity measurements

We present systematic investigations on the physics, detection performance and inversion of logging-while-drilling extra-deep azimuthal resistivity measurements (EDARM). First, the definitions of EDRAM measurements are discussed, followed by the derivation of the attenuation and phase-shift geometrical factors to illustrate the relative contributions of formation units to the observed signals. Then, a new definition of detection depth, which considers the uncertainty of inversion results caused by the data noise, is proposed to quantify the detection capability of EDARM. Finally, the Bayesian theory associated with Markov chain Monte Carlo sampling is introduced for fast processing of EDARM data. Numerical results show that EDARM is capable of detecting the azimuth and distance of remote bed boundaries, and the detection capability increases with increasing spacing and resistivity contrast. The EDARM tool can accommodate a large range of formation resistivity and is able to provide the resistivity anisotropy at arbitrary relative dipping angles. In addition, multiple bed boundaries and reservoir images near the borehole are readily obtained by using the Bayesian inversion.

Finite element simulations of logging-while-drilling and extra-deep azimuthal resistivity measurements using non-fitting grids

We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting grids when the geometry is complex. On the other side, fitting grids have been historically preferred because they offer additional accuracy for a fixed problem size in the general case. In this work, we analyse the use of non-fitting grids to simulate the response of logging instruments that are based on magnetic field resistivity measurements using 2.5D Maxwell’s equations. We provide various examples demonstrating that, for these applications, if the finite element matrix coefficients are properly integrated, the accuracy loss due to the use of non-fitting grids is negligible compared to the case where fitting grids are employed.