Electromagnetic borehole fields in a layered, dipping‐bed environment with invasion

Howard, A.Q.; Chew, Weng Cho

doi:10.1190/1.1443259

Cited by 28 publications

(7 citation statements)

References 14 publications

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“…6a shows that the apparent thickness of the bed of interest becomes large with the dipping angle, and the curve amplitude becomes large, too. Meanwhile, the so-called "polarization angle" begins to emerge on the high-angle curves, which is mainly due to the accumulated surface charge at the formation boundaries [22] . In Figs.…”

Section: Conductivity Averaging Formulamentioning

confidence: 99%

Application of the Staggered Grid Finite Difference Method to the Computation of 3D Induction Logging Response

Wang

Geng-ji

Cui

et al. 2003

Chinese J of Geophysics

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The finite difference method based on staggered grids is applied to simulate the induction logging response in 3D media. The invariance property of the Krylov subspace is used to solve the resulting large sparse complex symmetric linear system. To improve iteration convergence the pseudo inverse of the coefficient matrix is employed when constructing the Krylov subspace instead of the coefficient matrix itself. In each iteration four 3D Poisson equations are computed to get a new Lanczos vector with the incomplete Cholesky decomposition conjugate method. Generally the desirable solution is achieved with the iteration less than 20 times. Also, a new material averaging formula is proposed to get a reasonable average of the conductivity, which guarantees the conservation of the electric current.

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Section: Conductivity Averaging Formulamentioning

confidence: 99%

Application of the Staggered Grid Finite Difference Method to the Computation of 3D Induction Logging Response

Wang

Geng-ji

Cui

et al. 2003

Chinese J of Geophysics

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“…To this end, we will formulate the integral equation in (6) in the oblique (nonorthogonal) basis. Before discussing the transformation of the integral equation, we first write it as (11) where the vector is given by (12) in which the normalized vector potential is given by (13) The scalar Green function is given by (14) III. TRANSFORMATION PROCEDURE As shown in Fig.…”

Section: Basic Equations and Integral Representationsmentioning

confidence: 99%

“…Eigenfunction solutions to dipping-bed induction response are given by Hardman and Shen [10], Anderson et al [4], and Gianzero and Su [9]. The 3-D forward modeling of the induction response is given by Howard and Chew [11] and Anderson et al [5]. A one-dimensional (1-D) inversion method with dip is given by Minerbo [14].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear inversion in electrode logging in a highly deviated formation with invasion using an oblique coordinate system

Abubakar

Berg

2000

IEEE Trans. Geosci. Remote Sensing

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Abstract-Electrode logging as known in the oil industry is a method for determining the electrical conductivity distribution around a borehole or between two boreholes from the static-field (dc) measurements in the borehole. In this paper , we discuss the reconstruction of the three-dimensional (3-D) conductivity around a borehole in a highly deviated formation with invasion. At this moment, we have not included the borehole effect. To solve this problem, the full vector analysis is required. In most available algorithms, for the forward and inverse modeling of the resistivity data, the dipping bed environment is approximated using the staircase-discretization grid. In contrast, we have modeled the dipping-bed environment by introducing an oblique (nonorthogonal) coordinate system. By using the oblique coordinate system, we have gained some advantages over the usual approach. First, the use of the staircasing approximation for the dipping-bed environment can be avoided. This means that we reduce the discretization error, and we can suffice with less discretization points to obtain the results with the same degree of accuracy as the problem formulated in the Cartesian coordinate system. Secondly, the horizontally-symmetry constraints of the conductivity distribution can be included easily in the inversion procedure. Several numerical results are presented to demonstrate the performance of the inversion method using the synthetic "measured" data, which are generated by solving a forward-scattering problem numerically with the help of the conjugate gradient fast fourier transform (CGFFT) method.Index Terms-Electrode logging, nonlinear inversion, oblique coordinate system, three-dimensional method.

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“…Kaufman & Keller (1989) observed that the distance between "horns" is equal to the bed thickness plus the coil spacing. Howard & Chew (1992) showed theoretically, and Carvalho & Verma (1994) showed experimentally, through test tank measurements, that these oscillations on the logs are damped if the presence of the borehole and invasion are taken into account. Figure 10 shows the vertical profiles of the (a) coaxial and (b) coplanar arrays to an inclined bed sequence or a deviated borehole.…”

Section: Vertical Investigationsmentioning

confidence: 99%

Fundamentals of coaxial and coplanar coil arrays in induction tools

Carvalho¹,

Santos²,

Régis³

2010

Rev. Bras. Geof.

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ABSTRACT. Until about ten years ago, all commercial borehole induction devices were built up with the traditional coaxial coil arrays. Since then, those apparatus incorporated the unconventional coplanar coil arrays, in order to investigate thinly laminated reservoirs and to locate axially asymmetrical anomalies like vugs and fractures. In order to comprehend the fundamentals of the coplanar array in induction probes, we present a comparative study with the coaxial array through onedimensional modeling of some borehole environments, like: 1) homogeneous, isotropic and unlimited conducting media; 2) invaded thick bed with annulus; 3) horizontal and dipping multilayer sequences; 4) gradational transition zone between two thick beds; and 5) thinly laminated formations. The comparative study allows us to conclude that: 1) the skin effect is strongest in the coplanar array responses; 2) the coplanar array responses are more sensitive to mud filtrate invasion and annulus zones, which are direct indicators of movable oil; 3) polarization "horns" on the coplanar array profiles can be good bed boundary indicators; 4) coplanar arrays present the greatest sensitivity to detect and delineate thinly laminated reservoirs.Keywords: well logging, induction tools, thinly reservoirs, coplanar array. RESUMO.Por meio século, dede sua criação, todas as sondas comerciais por indução eletromagnética (EM) utilizavam o tradicional arranjo coaxial de bobinas.Somente a partir da virada do século XX que estas sondas passaram a incorporar o arranjo coplanar, devidoà necessidade de investigar reservatórios finamente laminados ou anomalias sem simetrias de rotação (fraturas ou cavidades). Com o objetivo de melhor compreender a aplicação do arranjo coplanar nas sondas de indução, elaboramos um estudo comparativo de suas respostas com as do tradicional arranjo coaxial, através de modelagem unidimensional, em alguns ambientes comunsà geofísica de poço: 1) meios homogêneos, isotrópicos e ilimitados; 2) camadas espessas com invasão de filtrado de lama e formação de annulus; 3) sequências de multicamadas horizontais e inclinadas; 4) transição gradacional entre duas camadas espessas; e 5) formações finamente laminadas. Este estudo comparativo entre os arranjos coaxial e coplanar permite concluir que: 1) o efeito pelicularé mais acentuado nas respostas do arranjo coplanar; 2) as respostas do arranjo coplanar são mais sensíveis a movimentação de fluidos na formação, principalmente nas zonas de annulus; 3) os perfis do arranjo coplanar apresentam picos devidosà polarização nas interfaces, que podem ser bons indicadores das fronteiras entre camadas; 4) o arranjo coplanaré mais sensível para detectar e delinear reservatórios finamente laminados.Palavras-chave: perfilagem em poço, ferramentas de indução, reservatório laminado, arranjo coplanar.

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Electromagnetic borehole fields in a layered, dipping‐bed environment with invasion

Cited by 28 publications

References 14 publications

Application of the Staggered Grid Finite Difference Method to the Computation of 3D Induction Logging Response

Application of the Staggered Grid Finite Difference Method to the Computation of 3D Induction Logging Response

Nonlinear inversion in electrode logging in a highly deviated formation with invasion using an oblique coordinate system

Fundamentals of coaxial and coplanar coil arrays in induction tools

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