Modeling electromagnetics on cylindrical meshes with applications to steel-cased wells

Heagy, Lindsey J.; Oldenburg, Douglas W.

doi:10.1016/j.cageo.2018.11.010

Cited by 29 publications

(14 citation statements)

References 58 publications

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“…In each of the wells, we observe that there is an increase in charge density near the end of the discontinuity along the length of the well. This was also noted in Griffiths & Li (1997) and Heagy & Oldenburg (2019) and is attributed to edge-effects.…”

Section: Basic Experimentsmentioning

confidence: 53%

“…All of the numerical simulations are run with the open source software described in Heagy & Oldenburg (2019), which relies on the electromagnetics module within SimPEG (Cockett et al 2015;Heagy et al 2017). In Heagy & Oldenburg (2019), we demonstrate validation of the code by comparing a time-domain EM simulation, which uses the same DC resistivity forward simulation code as used in this paper to compute the initial condition, with solutions presented in Commer et al (2015) as well as with the Finite Volume OcTree code described in Haber et al (2007).…”

Section: Governing Equations and Numerical Modellingmentioning

confidence: 99%

“…The positive electrode is connected to the top of the casing and the return electrode is positioned 2 km away. To simulate the physics, the 3D cylindrical DC code described in Heagy & Oldenburg (2019) was employed. In To quantify the charge along the length of the well, we have plotted the charge as a function of depth for the intact well (black), flawed well (blue), and also a "short" well of 500 m length (grey dash-dot) in Figure 3a.…”

Section: Basic Experimentsmentioning

confidence: 99%

“…Other approaches in electromagnetics include approximating the well with a series of electric dipoles (Kohnke et al 2017;Patzer et al 2017). The 3D cylindrical forward simulation code described in Heagy & Oldenburg (2019) and used in this example can serve a tool for validating and refining an approach to achieve the desired level of accuracy.…”

Section: Cartesian Gridmentioning

confidence: 99%

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Direct current resistivity with steel-cased wells

Heagy

Oldenburg

2019

Geophysical Journal International

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The work in this paper is motivated by the increasing use of electrical and electromagnetic methods in geoscience problems where steel-cased wells are present. Applications of interest include monitoring carbon capture and storage and hydraulic fracturing operations, as well as detecting flaws or breaks in degrading steel-casings -such wells pose serious environmental hazards. The general principles of electrical methods with steel-cased wells are understood, and several authors have demonstrated that the presence of steel-cased wells can be beneficial for detecting signal due to targets at depth. However, the success of a DC resistivity survey lies in the details. Secondary signals might only be a few percent of the primary signal. In designing a survey, the geometry of the source and receivers, and whether the source is at the top of the casing, inside of it, or beneath the casing will impact measured responses. Also the physical properties and geometry of the background geology, target, and casing will have a large impact on the measured data. Because of the small values of the diagnostic signals, it is important to understand the detailed physics of the problem and also to be able to carry out accurate simulations. This latter task is computationally challenging because of the extreme geometry of the wells, which extend kilometers in depth but have millimeter variations in the ra-arXiv:1810.12446v2 [physics.geo-ph] 8 Jul 2019 2 Lindsey J. Heagy, Douglas W. Oldenburg dial direction, and the extreme variation in the electrical conductivity (typically 5-7 orders of magnitude between the casing and the background geology).In this paper, we adopt a cylindrical discretization for numerical simulations to investigate three important aspects of DC resistivity in settings with steel-cased wells.(1) We examine the feasibility of using a surface-based DC resistivity survey for diagnosing impairments along a well in a casing integrity experiment. This parameter study demonstrates the impact of the background conductivity, the conductivity of the casing, the depth of the flaw, and the proportion of the casing circumference that is compromised, on amplitude of the secondary electric fields measured at the surface.(2) Next, we consider elements of survey design for exciting a conductive or resistive target at depth. We show that conductive targets generate stronger secondary responses than resistive targets, and that having an electrical connection between the target and well can significantly increase the measured secondary responses.(3) Finally, we examine common strategies for approximating the fine-scale structure of a steel cased well with a coarse-scale representation to reduce computational load. We show that for DC resistivity experiments, the product of the conductivity and the cross-sectional area of the casing is the important quantity for controlling the distribution of currents and charges along its length.To promote insight into the physics, we present results by plotting the currents, charges, and electric fi...

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Section: Basic Experimentsmentioning

confidence: 53%

Section: Governing Equations and Numerical Modellingmentioning

confidence: 99%

Section: Basic Experimentsmentioning

confidence: 99%

Section: Cartesian Gridmentioning

confidence: 99%

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Direct current resistivity with steel-cased wells

Heagy

Oldenburg

2019

Geophysical Journal International

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“…A well-known example is the Transforming expensive EM kernels 1337 aforementioned land or shallow marine case versus the deep marine case, where in the former case a dominating airwave has to be accurately modelled, whereas it can be completely ignored in the latter case. Recent areas of particular interest in time-domain modelling that pose numerical challenges are, for instance, simulating the fields through steel-cased wells (Heagy & Oldenburg 2019) or the effects of induced polarization (Kang et al 2020). The former is challenging because of the high conductivity contrasts requiring very detailed meshing, the latter is challenging for time-domain modelling because the models are frequency dependent.…”

Section: Introductionmentioning

confidence: 99%

Fast Fourier transform of electromagnetic data for computationally expensive kernels

Werthmüller

Mulder

Slob

2021

Geophysical Journal International

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SUMMARY 3-D controlled-source electromagnetic data are often computed directly in the domain of interest, either in the frequency domain or in the time domain. Computing it in one domain and transforming it via a Fourier transform to the other domain is a viable alternative. It requires the evaluation of many responses in the computational domain if standard Fourier transforms are used. This can make it prohibitively expensive if the kernel is time-consuming as is the case in 3-D electromagnetic modelling. The speed of modelling obtained through such a transform is defined by three key points: solver, method and implementation of the Fourier transform, and gridding. The faster the solver, the faster modelling will be. It is important that the solver is robust over a wide range of values (frequencies or times). The method should require as few kernel evaluations as possible while remaining robust. As the frequency and time ranges span many orders of magnitude, the required values are ideally equally spaced on a logarithmic scale. The proposed fast method uses either the digital linear filter method or the logarithmic fast Fourier transform together with a careful selection of evaluation points and interpolation. In frequency-to-time domain tests this methodology requires typically 15–20 frequencies to cover a wide range of offsets. The gridding should be frequency- or time-dependent, which is accomplished by making it a function of skin depth. Optimizing for the least number of required cells should be combined with optimizing for computational speed. Looking carefully at these points resulted in much smaller computation times with speedup factors of ten or more over previous methods. A computation in one domain followed by transformation can therefore be an alternative to computation in the other domain domain if the required evaluation points and the corresponding grids are carefully chosen.

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