Oilfield exploration and production drilling companies commonly use Logging-While-Drilling (LWD) measurements provided by propagation-resistivity tools. These tools emit radio waves at frequencies from 400 kHz to 2 MHz and measure signal attenuation and phase shift between receiver pairs. In this frequency range, the measurements are sensitive to both the electric conductivity and dielectric permittivity in surrounding rock formations. Tool response to these two parameters has been characterized by modeling and is well known after many decades of study and analysis.
However, dielectric permittivity as a formation parameter is still poorly understood. Over the frequency range in question, the permittivity shows considerable dispersion. The first-order effect of dispersion is to decrease as frequency increases. In addition, laboratory studies under controlled conditions have shown that several competing effects of grain-surface structure and metallic inclusion combine and distort the dielectric signature of the propagation-resistivity measurements. Also, fluid parameters can introduce surface effects. Clearly, there is no simple petrophysical answer to such a complex formation response.
One way to analyze the problem is to directly invert the measured attenuation and phase shift data to obtain formation conductivity and permittivity. The inversion must be separately performed at each operating frequency to account for dispersion. The algorithm described in this paper was developed anew from previously published work by rederiving the solution from Maxwell's equations in a more computationally efficient manner. The inversion provides independent conductivity/resistivity log curves and permittivity log curves.
For quality control, the dielectrically inverted resistivity curves are compared to the conventionally processed phase-shift and attenuation resistivity curves. The dielectrically inverted resistivity will always fall between the two conventionally processed resistivities.
There is no simple relationship between the dispersive, frequency dependent permittivity and any formation or fluid parameter, comparable to Archie's simple water-saturation relationship. Both microscopic and macroscopic formation parameters contribute to dispersion: water-filled porosity, cation exchange capacity (CEC), conductive minerals, and formation factor. Past studies in research and in log interpretation have provided some insights on these reservoir property dependencies of permittivity in shaly sands. On the other hand, carbonate rocks with their widely varying pore structure impose additional uncertainties. Still, there appear some underlying common trends among many logs studied to date with dielectric inversion quantities.
On the reservoir scale, dielectric measurements in general have proven to be a useful tool for estimating water saturation independently of water salinity. Dielectric inversion of LWD array propagation measurements provides this information at radial depths away from the borehole wall much deeper than the dedicated wireline GHz-pad tools. Thus, the water-saturation estimates from array tools may indicate hydrocarbons even in the presence of deeper invasion.
The new dielectric-inversion algorithm accommodates any vendor's axisymmetric LWD propagation-resistivity array tool that is featured in the SPWLA Resistivity-SIG catalogue. The dielectric inversion has been successfully applied to legacy logs. It applies equally well to real-time processing while drilling. It will hopefully fill a missing gap between raw tool measurements and true petrophysical interpretation.
