Sensitivity of dipole magnetic tomography to magnetic nanoparticle injectates
Abstract We compare the sensitivity of magnetic field measurements to perturbations of magnetic permeability with the field sensitivity to conductivity alterations. The conductivity perturbations can be caused by the different conductivity of the injected and formation resident fluid and the magnetic permeability perturbations by injecting magnetic nanoparticles. We devise a simple method for calculating the magnetic permeability sensitivity required to solve parametric inverse problems in electromagnetic (EM) tomography involving magnetic permeability perturbations. We apply the method in 3D and 2D axisymmetric to both crosswell and single-well configurations in a homogeneous background. The emphasis of this paper is on measurements acquired at very low induction numbers (kr ≪ 1; k being the wave number and r the distance) where the wave length or the skin depth becomes an irrelevant scale. The sensitivity to magnetic permeability perturbations is significantly higher than conductivity perturbations at low frequencies. Furthermore, at the low-frequency regime, the magnetic permeability sensitivity is largely independent of frequency, unlike the conductivity sensitivity which improves with frequency, consistent with quasi-static dipole magnetics. The sensitivity patterns for conductivity and magnetic permeability are quite different. The four lobes with opposite signs surrounding the source and receiver in case of magnetic permeability provide opportunities for vertical discrimination of magnetic measurements. In the case of a single-well configuration, the sensitivity to magnetic permeability perturbation is larger close to the wellbore than conductivity. Also, the sign reversals of both real and imaginary parts of the magnetic permeability enhance the horizontal sensitivity of the magnetic measurements. The geometry of the problem also affects the sensitivities quite significantly. Both 3D and 2D axisymmetric are considered in this study. The geometrical spreading of the perturbed region in the axisymmetric case suppresses the sensitivity value for both conductivity and magnetic permeability. The magnetic permeability perturbations exhibit a higher sensitivity when the magnetic contrast agents are in the proximity of the source and receivers (or near the wellbore in case of single-well). On the other hand, EM measurements are more sensitive to conductivity perturbations in the interwell region in the case of a crosswell and off-wellbore in the case of a single-well system at moderate and high frequencies.