A Priori Fourier Analysis for 2.5D Finite Elements Simulations of Logging-While-Drilling (LWD) Resistivity Measurements

The depth of detection (DOD), which is an important concept in logging data interpretation, describes the detection capability of the borehole measurements. We have extended the definition of DOD for azimuthal information, namely, the geosignal delivered by azimuthal resistivity tools, to resistivity logs in logging-while-drilling (LWD) applications. Instead of using the radial geometric factor, the detection thresholds in predicting a geologic boundary are used to describe the DOD of a measurement. This definition unifies the criteria to evaluate the detectability of different borehole measurements, such as LWD resistivity measurements and geosignals. It also can be generalized to other kinds of well logging methods in LWD applications. Using the proposed definition, we analyze the detection capability of the LWD resistivity measurements in looking-around and looking-ahead applications; they provide more tangible descriptions. In vertical or near-vertical wells, the definition provides an indicator to evaluate the capability and reliability of looking ahead of deep/ultradeep LWD resistivity tools. The investigations on the influence of the DOD on the distance-to-boundary inversion, which can help in developing a robust and accurate inversion scheme, also are presented and discussed.

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Solving three-dimensional interface problems with immersed finite elements: A-priori error analysis

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110445 ◽

2021 ◽

pp. 110445

Author(s):

Ruchi Guo ◽

Xu Zhang

Keyword(s):

Finite Elements ◽

Error Analysis ◽

A Priori ◽

Three Dimensional ◽

Interface Problems ◽

A Priori Error Analysis ◽

Immersed Finite Elements

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REAL-TIME 2.5D INVERSION OF LWD RESISTIVITY MEASUREMENTS USING DEEP LEARNING FOR GEOSTEERING APPLICATIONS ACROSS FAULTED FORMATIONS

10.30632/spwla-2021-0104 ◽

2021 ◽

Author(s):

Kyubo Noh ◽

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Carlos Torres-Verdín ◽

David Pardo ◽

◽

...

Keyword(s):

Deep Learning ◽

Real Time ◽

Fault Plane ◽

Synthetic Data ◽

Field Measurements ◽

Geological Structure ◽

Inversion Method ◽

Adaptive Finite Element ◽

Resistivity Measurements ◽

Lwd Resistivity

We develop a Deep Learning (DL) inversion method for the interpretation of 2.5-dimensional (2.5D) borehole resistivity measurements that requires negligible online computational costs. The method is successfully verified with the inversion of triaxial LWD resistivity measurements acquired across faulted and anisotropic formations. Our DL inversion workflow employs four independent DL architectures. The first one identifies the type of geological structure among several predefined types. Subsequently, the second, third, and fourth architectures estimate the corresponding spatial resistivity distributions that are parameterized (1) without the crossings of bed boundaries or fault plane, (2) with the crossing of a bed boundary but without the crossing of a fault plane, and (3) with the crossing of the fault plane, respectively. Each DL architecture employs convolutional layers and is trained with synthetic data obtained from an accurate high-order, mesh-adaptive finite-element forward numerical simulator. Numerical results confirm the importance of using multi-component resistivity measurements -specifically cross-coupling resistivity components- for the successful reconstruction of 2.5D resistivity distributions adjacent to the well trajectory. The feasibility and effectiveness of the developed inversion workflow is assessed with two synthetic examples inspired by actual field measurements. Results confirm that the proposed DL method successfully reconstructs 2.5D resistivity distributions, location and dip angles of bed boundaries, and the location of the fault plane, and is therefore reliable for real-time well geosteering applications.

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Parallel tempered trans-dimensional Bayesian inference for the inversion of ultra-deep directional logging-while-drilling resistivity measurements

Journal of Petroleum Science and Engineering ◽

10.1016/j.petrol.2020.106961 ◽

2020 ◽

Vol 188 ◽

pp. 106961 ◽

Cited By ~ 2

Author(s):

Qiuyang Shen ◽

Jiefu Chen ◽

Xuqing Wu ◽

Zhu Han ◽

Yueqin Huang

Keyword(s):

Bayesian Inference ◽

Resistivity Measurements ◽

Logging While Drilling

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On Superconvergence of a Gradient for Finite Element Methods for an Elliptic Equation with the Nonsmooth Right–hand Side

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2002-0018 ◽

2002 ◽

Vol 2 (3) ◽

pp. 295-321 ◽

Cited By ~ 3

Author(s):

Alexander Zlotnik

Keyword(s):

Finite Elements ◽

Elliptic Equation ◽

Error Estimates ◽

Dirichlet Boundary ◽

A Priori ◽

Boundary Function ◽

Right Hand ◽

Priori Error Estimates ◽

The Right ◽

2D And 3D

AbstractThe elliptic equation under the nonhomogeneous Dirichlet boundary condition in 2D and 3D cases is solved. A rectangular nonuniform partition of a domain and polylinear finite elements are taken. For the interpolant of the exact solution u, a priori error estimates are proved provided that u possesses a weakened smoothness. Next error estimates are in terms of data. An estimate is established for the right–hand side f of the equation having a generalized smoothness. Error estimates are derived in the case of f which is not compatible with the boundary function. The proofs are based on some propositions from the theory of functions. The corresponding lower error estimates are also included; they justify the sharpness of the estimates without the logarithmic multipliers. Finally, we prove similar results in the case of 2D linear finite elements and a uniform partition.

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