Petrophysical interpretation of logging-while-drilling borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects

Abstract

Petrophysical interpretation of logging-while-drilling (LWD) borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects remains a challenge in formation evaluation. In high-angle and horizontal (HAHZ) wells penetrating electrically anisotropic sandstones, phase and attenuation apparent resistivity logs often exhibit values larger than resistivity parallel to bedding planes. Consequently, traditional interpretation methods often fail to accurately estimate hydrocarbon saturation when using only the long-spacing phase apparent resistivity log (P40H) in petrophysical calculations. We implement two approaches (analytical and Bayesian) to estimate horizontal and vertical resistivities from apparent resistivity measurements. The first analytical approach is based on the numerical simulation of LWD resistivity measurements using synthetic models under various conditions of electrical anisotropy and well inclination to derive analytical models. The relative error of analytical approximations is less than 6%. In the presence of measurement noise and shoulder-bed effects, we implement a Bayesian method for well-log inversion and uncertainty quantification. The relative error of Bayesian inversion is less than 2%. Estimates of horizontal and vertical resistivities then can be used for petrophysical analysis. A challenging set of synthetic and field examples of HAHZ wells penetrating electrically anisotropic formations is selected for examination and verification of the new methods. For radial lengths of invasion less than 20 cm (8 in), sensitivity analysis indicates that the effects of conductive mud-filtrate invasion on long-spacing resistivity logs are negligible. The long-spacing phase (P40H) and attenuation (A40H) apparent resistivities are used to estimate horizontal and vertical resistivities. In the field examples under study, electrical anisotropy is caused by intercalated laminations of coarse- and fine-grained sandstones; the volumetric concentration of shale is negligible. Considering that Archie’s parameters are direction dependent, sensitivity analysis indicates that the effective value of the saturation exponent parallel to bedding planes is less sensitive to the volumetric concentration of fine-grained sandstone layers compared with the saturation exponent perpendicular to bedding planes. Thus, water saturation of grain-laminated sandstones in HAHZ wells can be estimated using horizontal resistivity with Archie’s parameters that are consistent with petrophysical interpretations performed in vertical wells. Estimates of water saturation in the field examples using horizontal resistivity agree with saturation-height models. Compared with conventional interpretation methods that use P40H as the formation resistivity, the new approach improved the estimation of hydrocarbon saturation by 10%.