Petrophysical Inversion of Resistivity Logging Data

Abstract Inversion is a powerful tool for interpreting resistivity-logging data in complex situations, such as deep invasion, high conductive shoulders, thin beds, anisotropic formations, and highly deviated and horizontal wells. Inversion also provides a general means to interpret data from earlier, unfocused resistivity tools as well as the new generation of array-type instruments, allowing for accurate delineation of the resistivity structure. Although, in most cases, inversion produces solutions that are consistent with petrophysics and geology, there are occasions where consistency is not achieved. In order to address these inconsistencies, we have developed a petrophysical inversion algorithm that involves gamma ray, neutron, density, acoustic, and resistivity data in a single, unified interpretation process. The steps in the interpretation process consist of estimating bed boundary positions from all available measurements, including gamma ray, neutron, density, and resistivity data, using a weighted inflection point method. Bed boundary positions are then adjusted using the tool response functions associated with the various instruments involved and integrated to produce a consistent set of bed boundaries, which best represents the subsurface geology and lithology. Next, upper and lower bounds for formation resistivity and flushed zone resistivity are estimated using an appropriate water saturation equation. Input for resistivity bound estimation includes shale volume, porosity, as well as the possible range of variation for water saturation, formation water resistivity, and shale resistivity. The resistivity bounds are incorporated into the inversion algorithm via an outside penalty function added to the original objective function of the optimization. The proposed inversion algorithm utilizes a generic objective function including a reference model and data weighting based on uncertainties. Furthermore, a first-order spatial-finite difference operator has been built into the objective function to eliminate unrealistic oscillations in the inversion results. A field case example shows that the proposed inversion process can effectively handle systematic noise in the data caused by borehole washouts and inappropriate bed boundary positioning, and generates petrophysically meaningful inversion results.