Dielectric Dispersion Model for Qualitative Interpretation of Wettability

Formation dielectric dispersion is known to be affected by the formation wettability state. Typically, a hydrocarbon-wet formation has a reduced DC conductivity with a less dispersive permittivity response over a broad frequency range. In this work, we focus on how formation wettability changes affect complex dielectric dispersion in the frequency range (MHz to GHz) of a typical multifrequency downhole tool. The goal is to study the feasibility of inferring the formation wettability state using the dielectric dispersion obtained from downhole tools. To capture the effect of wettability changes, we adapt a physical picture characterizing the hydrocarbon-wet state by the presence of effective trapped water droplets isolated from a continuous water phase. By modifying the conventional bimodal-like models, we establish a new class of dielectric dispersion models that includes the trapped water fraction as an additional model parameter. Thus, the modeled dielectric dispersion is controlled by a few key petrophysical parameters: the water-filled porosity, the brine salinity, the water phase tortuosity exponents, and the trapped water fraction. Our model construction shows that we can clearly relate the trapped water fraction to the wettability state of the rock. When the trapped water fraction approaches zero, the new model naturally reduces to the water-wet limit. In contrast, a significant fraction of trapped water indicates that the formation is in a more hydrocarbon-wet state. The trapped water fraction is designed as the sole model parameter indicating the formation wettability state. Hence, we can better examine whether the model response with respect to the trapped water fraction can be correlated to the wettability changes. By comparing dielectric dispersions of cores before and after core wettability changes from water-wet to hydrocarbon-wet, our new model can explain the data with wettability changes more parsimoniously than conventional models. However, for practical applications, it is still difficult to employ a straightforward inversion scheme to unambiguously determine the wettability changes from inverted values of trapped water fraction. This is due to limited information content of the dielectric signal that does not support the independent inference of all desired petrophysical parameters. Instead, we found a phenomenological feature, established through a self-consistent model study and benchmarked with experimental data, that correlates with wettability changes. By fixing the trapped water fraction value and fitting the model to dielectric dispersion, the inverted total water-filled porosity increases monotonically with the increased trapped water fraction for water-wet cores but remains constant for hydrocarbon-wet cores. Intuitively, water-wet formations have a fully connected water phase, which requires enough connected water volume to fit dielectric dispersions and leads to the monotonical increase of the inverted total water-filled porosity. In contrast, forcing a sufficient connected water phase is not required for fitting the dielectric dispersion of hydrocarbon-wet formations due to the presence of effectively trapped water. The observation of this feature in the newly constructed model enables us to establish a workflow for delineating whether the formation is predominately water-wet or hydrocarbon-wet with the downhole dielectric tools.