Integrating Thomas-Stieber with a Staged Differential Effective Medium Model for Saturation Interpretation of Thin-Bedded Shaly Sands



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A Staged Differential Effective Medium (SDEM) model based on the Hanai-Bruggeman equation is applied to interpret water saturation in shaly sands. In this model, the conductivity of the formation changes when different volumes of clays, oil, and quartz (inclusions) are successively distributed in the host. The host continuously varies as the inclusions are added. The resulting equations require the conductivity and distribution parameters, which are assumed constant as the inclusion is added. A Thomas-Stieber analysis allows the separation of clay types that are distributed at different length scales. It allows estimating the fractional bulk volumes of clay laminations and dispersed clays using only the density and gamma ray log data. The three endpoints of the Thomas-Stieber triangle (clean sand, 100 percent clay-filled sand, and shale) are determined from log data, thin sections, and SEM (Scanning Electron Microscope) observations. Dispersed clay and shale laminae porosity were estimated using SEM imaging. The dispersed clays were observed to have substantially higher porosity than the laminar clays. For this reason, clay laminae and pore-filling dispersed clays are allowed to have differing properties. This is a generalization of the conventional Thomas-Stieber model. Principal Component Analysis (PCA) was used to cluster the data, allowing the impact of clays and their occurrence to be assessed. The density, resistivity, acoustic, and gamma ray logs are employed for this analysis. The model is applied iteratively to extract the clays, oil, and quartz properties according to their differing length scales. The initial regression determines the distribution parameter and resistivity of the shale laminae. Next, the properties of the clay-filled sand are determined. The clay-filled sand conductivity increases linearly with the amount of dispersed clay. The pore fluid salinity is then estimated and agrees well with produced water analyses. Finally, the water saturation in the shaly sand is estimated. Saturation estimations using the SDEM model differ from those obtained using conventional shaly sand resistivity models. The water saturation estimations using the SDEM model are in agreement with the capillary pressure estimates, unlike the conventional shaly sand models. These results are consistent with the current understanding of column heights and free water levels in the formation.



Shaly sands, Staged Differential Effective Medium model, SDEM, T