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Macroscopic Electrical Anisotropy of Laminated Reservoirs: A Tensor Resistivity Saturation Model

Accurate petrophysical evaluation of deep water turbidites composed of thin bedded sand-shale sequences is crucial in the economic decision to explore, develop, and produce these reservoirs. Traditional laminar shaly sand saturation equations are based on a parallel conductivity model that typically results in significant underestimation of in-place hydrocarbons. Electrical anisotropy is the macroscopic effect of thinly layered sedimentary formations in which logging tools have insufficient vertical resolution to properly resolve individual beds or laminae. Utilizing anisotropy in the saturation analysis transforms the classic low resistivity shaly sand problem into a tensor petrophysical model. The tensor shaly sand saturation model is applied to both simple and complex reservoir types with the following results: 1. Simple laminated sand-shale model: Forward model calculations for the resistivity tensors demonstrate the effect of the model variables on net-to-gross, shale resistivity, sand resistivity, and sand porosity. Sand saturation determination is dominated by the vertical component and shale resistivity is dominated by the horizontal component. 2. Complex anisotropic sand model: Forward modeling using alternating fine-coarse grain size distributions within a sand body demonstrates the effect of pore size changes resulting in capillary-induced water saturation profiles. Tensor components for anisotropic sands are presented as an integral expression for any water saturation distribution. The following response of the Resistivity Index (RI) is noted: ○ RI vs. S w relationship does not follow an Archie-type power law ○ RI vs. S w relationship is different for the parallel and perpendicular laminated resistivity components. The tensor water saturation equation utilizing electrical anisotropy is demonstrated to be theoretically correct for both the laminar sand-shale reservoirs and complex anisotropic sand reservoirs. The significant advantage of the tensor model is a more accurate water saturation determination that minimizes the errors inherent in traditional parallel conductivity saturation equations.