Simulations of 3D DC borehole resistivity measurements with a goal-oriented <Emphasis Type="Italic">hp</Emphasis> finite-element method. Part II: through-casing resistivity instruments |
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| Authors: | D Pardo C Torres-Verdín M Paszynski |
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| Institution: | (1) Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, CPE 5.168A, Speedway and 26th, Austin, TX 78712, USA;(2) Department of Computer Science, AGH University of Science and Technology, Krakow, Poland |
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| Abstract: | We simulate direct current (DC) borehole resistivity measurements acquired in steel-cased deviated wells for the assessment
of rock formation properties. The assumed data acquisition configuration considers one current (emitter) and three voltage
(collector) electrodes that are utilized to measure the second difference of the electric potential along the well trajectory.
We assume a homogeneous, 1.27-cm-thick steel casing with resistivity equal to 10 − 5 Ω· m. Simulations are performed with two different numerical methodologies. The first one is based on transferring two-dimensional
(2D) axisymmetric optimal grids to a three-dimensional (3D) simulation software. The second one automatically produces optimal
3D grids yielded by a 3D self-adaptive goal-oriented algorithm. Both methodologies utilize high-order finite elements (FE)
that are specially well-suited for problems with high-contrast coefficients and rapid spatial variations of the electric field,
as it occurs in simulations that involve steel-cased wells. The method based on transferring 2D-optimal grids is efficient
in terms of CPU time (few seconds per logging position). Unfortunately, it may produce inaccurate 3D simulations in deviated
wells, even though the error remains below 1% for the axisymmetric (vertical) well. The method based on optimal 3D grids,
although less efficient in terms of CPU time (few hours per logging position), produces more accurate results that are validated
by a built-in a posteriori error estimator. This paper provides the first existing simulations of through-casing resistivity
measurements in deviated wells. Simulated resistivity measurements indicate that, for a 30° deviated well, measurements in
conductive layers 0.01 Ω· m) are similar to those obtained in vertical wells. However, in resistive layers (10,000 Ω· m),
we observe 100% larger readings in the 30° deviated well. This difference becomes 3,000% for the case of a 60° deviated well.
For this highly-deviated well, readings corresponding to the conductive formation layer are about 30% smaller in magnitude
than those in a vertical well. Shoulder effects significantly vary in deviated wells. |
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| Keywords: | Electrostatics hp finite elements Exponential convergence Goal-oriented adaptivity Trough-casing resistivity instruments |
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