Analytical solutions of EM fields due to a dipolar source inside an infinite casing

Abstract

This paper studies the problem of electromagnetic fields observed outside of an infinite metallic casing due to dipolar excitations inside the pipe. Closed-form expressions are derived for the hertz vector potential driving the solution of the boundary value problem. The results indicates that the fields outside the casing are due to a distribution of vertical dipoles that decay in strength away from the true source. Analytical expressions are also obtained for the induced source distribution, as a function of the geometry and electric properties of the system. For the transverse magnetic mode (electric dipole source), the sources represent an electric current channeled vertically along the casing, whereas for the transverse electric mode (magnetic dipole source), they represent a distribution of induced magnetic moments. The strength of the current channeling decays exponentially away from the source, whereas the strength of the induced magnetic moment drops within the first few meters. The expressions obtained for the fields due to a magnetic dipole reveals that the effect of the casing yields a multiplicative complex constant, which attenuates the dipolar-type field. This effect has been observed experimentally in crosswell surveys, but it has never been formally proven. The fields due to an electric dipole excitation describe an inhomogeneous cylindrical surface wave propagating and attenuating in the radial and vertical directions.

Three-Dimensional Modeling of the Casing Effect in Onshore Controlled-Source Electromagnetic Surveys

“…Along the length of the casing, the amplitude of the field decreases exponentially away from the well with the spatial rate of decay depending on the conductivity of the surrounding formations. Cuevas (2014) studied the EM fields generated by a dipolar source placed inside an infinite casing and presented the approximate analytical solutions that illustrate the dependence of the fields on the various parameters of the model, thus providing a physical insight on the spatial distribution of the fields as well as on the physical behavior of the sources. Recently, the analysis of the casing effect has been extended in Cuevas (2016) to the channeling arising from the source-induced currents in pipes that extend horizontally in front of the dipolar antennas.…”

Finite-element analysis of top-casing electric source method for imaging hydraulically active fracture zones

“…Its conductivity value is determined such that the crosssectional conductance of the prism is kept same as the hollow well. The well can also be replaced with a series of small electric dipoles along the well in the DC and frequency domain (Cuevas, 2014;Nieuwenhuis et al, 2015). Weiss 2017 others.…”

Electrical and electromagnetic responses over steel-cased wells

“…This approximation will begin to break down if the size of the prism approximating the casing has a larger area than the true casing. To overcome this, several alternative approaches have been developed, including replacing the casing with a distribution of charges (Weiss et al, 2016) or dipoles (Cuevas, 2014). Other modelling approaches include using a resistor network approach (Yang et al, 2016), OcTree meshes to locally refine around the casing (Haber et al, 2016), and the development of hierarchical finite element approach (Weiss, 2017), among others.…”