Dielectric logging with downhole invasion effects

The transfer impedance between conducting coils is evaluated to estimate the downhole dielectric properties that can contribute to more effective exploration and production of gas/oil reservoirs. The earth formation with a borehole-mud filtrate invasion is simulated by concentric zones of variable dielectric properties to account for rocks saturated by different fluids. We have imposed analytical restrictions to allow only magnetic-dipole coupling between logging coils and to limit logging source frequencies from 10 to 30 MHz for typical coil spacings. Depending on the depth of invasion front, guided waves may exist in the invaded formation. When guided waves do not exist, rapidly converging branchcut integrations are used to evaluate the transfer impedance. When the invasion front begins to support guided waves the numerical convergence becomes somewhat slower using spatial-band-limited integrations. Both types of integration are used to produce inversion charts from which dielectric properties and invasion-front radii can be estimated from downhole-measurable transfer impedances. Ambiguity in parameter inversion is also demonstrated to provide insight for developing a future inverse process based on array processing of adequately sampled data.