A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling

/pdf/a-goal-oriented-adaptive-finite-element-approach-for-plane-2zntxylft7.pdf

The application of unstructured grids can improve the solution of total field electromagnetic problems because these grids allow efficient local refinement of the mesh at the locations of high field gradients. Unstructured grids also provide the flexibility required for representing arbitrary topography and subsurface interfaces. We investigated the generalization of the standard Yee’s staggered scheme to unstructured tetrahedral-Voronoi grids using a finite-volume approach. We discretized the Helmholtz equation for the electric field in the frequency domain and solved the problem to find the projection of the total electric field along the edges of the tetrahedral elements. To compute the electric and magnetic fields at the observation points, an interpolation technique was employed, which uses the edge vector interpolation functions of the tetrahedral elements. To verify the presented scheme, two examples were evaluated, which revealed the computation of the total and secondary fields due to ele...

A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

Including highly conductive steel infrastructure into electromagnetic (EM) earth modeling is motivated by the fact that long metal-cased boreholes have the potential to be used as boosting antennas that enable larger source dipole moments and greater signal penetration depths. Unfortunately, geophysical algorithms designed to simulate EM responses over rather regional scales are complicated by material property contrasts and structure geometries that are more typical for EM engineering applications. Hence, the great majority of earth-modeling algorithms that consider EM responses from steel-cased boreholes use integral-equation methods. To be able to model complex casing scenarios, we revisited the finite-difference time-domain (FDTD) method to advance the modeling of transient-EM field responses from steel-cased boreholes. A time-dependent function that allows for larger FDTD time steps in the DuFort-Frankel method was developed, alleviating the generally large computational overhead. We compared our method against three different kinds of benchmark solutions to demonstrate the reliability of the FDTD field solutions. These test cases were carried out to check the feasibility of a final hydraulic fracturing study. Images of the electric current distribution in a sheetlike rock fracture were calculated for the cases with and without the presence of a connecting borehole casing, demonstrating the casing’s potential of illuminating deep target zones.

Transient-electromagnetic finite-difference time-domain earth modeling over steel infrastructure

The study of electrical anisotropy in the Earth, defined as the electrical conductivity varying with orientation, has experienced important advances in the last years regarding the investigation of its origins, how to identify and model it, and how it can be related to other parameters, such as seismic and mechanical anisotropy This paper provides a theoretical background and a review of the current state of the art of electrical anisotropy using electromagnetic methods in the frequency domain, focusing mainly on magnetotellurics The aspects that will be considered are the modelling of the electromagnetic fields with anisotropic structures, the analysis of their responses to identify these structures, and how to properly use these responses in inversion and interpretation Also, an update on the most recent case studies involving anisotropy is provided

http://diposit.ub.edu/dspace/bitstream/2445/161860/1/617102.pdf

The Role of Electrical Anisotropy in Magnetotelluric Responses: From Modelling and Dimensionality Analysis to Inversion and Interpretation

To advance and optimize secondary and tertiary oil recovery techniques, it is essential to know the areal propagation and distribution of the injected fluids in the subsurface. We investigate the applicability of controlled-source electromagnetic methods to monitor fluid movements in a German oilfield (Bockstedt, onshore Northwest Germany) as injected brines (highly saline formation water) have much lower electrical resistivity than the oil within the reservoir. The main focus of this study is on controlled-source electromagnetic simulations to test the sensitivity of various source–receiver configurations. The background model for the simulations is based on two-dimensional inversion of magnetotelluric data gathered across the oil field and calibrated with resistivity logs. Three-dimensional modelling results suggest that controlled-source electromagnetic methods are sensitive to resistivity changes at reservoir depths, but the effect is difficult to resolve with surface measurements only. Resolution increases significantly if sensors or transmitters can be placed in observation wells closer to the reservoir. In particular, observation of the vertical electric field component in shallow boreholes and/or use of source configurations consisting of combinations of vertical and horizontal dipoles are promising. Preliminary results from a borehole-to-surface controlled-source electromagnetic field survey carried out in spring 2014 are in good agreement with the modelling studies.

Controlled‐source electromagnetic monitoring of reservoir oil saturation using a novel borehole‐to‐surface configuration

This paper describes the implementation and successful validation of a new staggered-grid, finite-difference algorithm for the numerical simulation of frequency-domain electromagnetic borehole measurements. The algorithm is basedonacoupledscalar-vectorpotentialformulationforarbitrary 3D inhomogeneous electrically anisotropic media. We approximate the second-order partial differential equations for the coupled scalar-vector potentials with central finite differences on both Yee’s staggered and standard grids. Thediscretizationofthepartialdifferentialequationsandthe enforcement of the appropriate boundary conditions yields a complex linear system of equations that we solve iteratively using the biconjugate gradient method with preconditioning. Theaccuracyandefficiencyofthealgorithmisassessedwith examples of multicomponent-borehole electromagnetic-induction measurements acquired in homogeneous, 1D anisotropic,2Disotropic,and3Danisotropicrockformations.The simulation examples consider vertical and deviated wells with and without borehole and mud-filtrate invasion regions. Simulation results obtained with the scalar-vector coupled potentialformulationfavorablycompareinaccuracywithresults obtained with 1D, 2D, and 3D benchmarking codes in the dc to megahertz frequency range for large contrasts of electricalconductivity.Ournumericalexercisesindicatethat the coupled scalar-vector potential equations provide a generalandconsistentalgorithmicformulationtosimulateborehole electromagnetic measurements from dc to megahertz in the presence of large conductivity contrasts, dipping wells, electrically anisotropic media, and geometrically complex modelsofelectricalconductivity.

Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials

Weusenumericalsimulationstoinvestigatethepossibility of enabling steel-cased wells as galvanic sources to detect and quantify spatial variations of electrical conductivity in the subsurface.The study assumes a vertical steel-cased well that penetrates electrically anisotropic horizontal layers. Simulations include a steel-cased vertical well with a finitelength thin wire of piecewise-constant electric conductivity and magnetic permeability.The steel-cased well is energized atthesurfaceorwithintheboreholeatanarbitrarydepthwith an electrode connected to a current source of variable frequency. Electromagnetic EM fields excited by the energized steel-cased well are simulated with an integral-equation approach. Results confirm the accuracy of the simulationswhenbenchmarkedagainstthewhole-spacesolutionof EM fields excited by a vertical electric dipole. Additional simulationsconsiderawiderangeoffrequenciesandsubsurfaceconductivityvaluesforseveraltransmitter-receiverconfigurations, including borehole-to-surface and crosswell. The distribution of electric current along the steel-cased well is sensitive to vertical variations of electric conductivity in thehostrock.Inaddition,numericalsimulationsindicatethat crosswell and borehole-to-surface receiver configurations couldreliablyestimateverticalvariationsofelectricconductivity within radial distances of up to 500 m for frequencies below 100 Hz and for average host rock electric conductivitiesbelow1 S /m.

1D subsurface electromagnetic fields excited by energized steel casing

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Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials

1D subsurface electromagnetic fields excited by energized steel casing