Physics Based Permeability Models Based on Thomas-Stieber Plots
Authors:   University of Houston, Horvath William , Myers Michael T. ,   University of Houston, Hathon Lori A. ,   University of Houston
Published: November 2024

A Staged Differential Effective Medium (SDEM) model is applied to interpret the permeability in thin-bedded shaly sands. In this model, the permeability varies with the amount and distribution of clay minerals. The model allows continuous interpolation between a series and parallel distribution of the clay minerals. Dispersed clays are added before structural clays and matrix grains. The longest length scale, clay laminations, are the last phase added to the massive sand matrix. The resulting equations include the distribution parameters for each inclusion. The standard Thomas-Stieber (T-S) model is extended to allow for differing clay properties. This more accurate analysis allows a quantitative separation of clay types that are distributed at these different length scales using only density and gamma ray log data. The three endpoints of the Thomas-Stieber triangle (clean sand, clay-filled sand, and shale) are determined from log data, thin sections, and scanning electron microscope (SEM) observations. Dispersed clay porosity and shale laminae porosity were estimated using SEM imaging and image segmentation. The dispersed clays were observed to have substantially higher porosity than the laminar clays. Clay laminae and pore-filling dispersed clays are, therefore, given differing porosities and gamma ray responses in contrast to a standard T-S model. The SDEM model is then used to iteratively extract the clay properties according to their differing length scales. The initial regression determines the distribution parameter of the shale laminae. The properties of the clay-filled sand allow the impact of the dispersed clays on permeability to be determined. Core data are used to calibrate the permeability model. Dispersed clay is found to reduce the permeability much more rapidly than clay laminations; sand macroporosity is more strongly correlated to permeability than the net/gross (N/G). Macroporosity is defined as the total percent bulk volume of macropores, or sand porosity minus the bulk volume fraction of dispersed clay. Macroporosity ranges from the total porosity in clean sand to zero when the dispersed clay is completely pore filling. Using macroporosity as the control on permeability acknowledges the negligible contribution of the microporosity associated with dispersed clays. The standard Timur-Coates parameters are not appropriate for use in this reservoir. Both the NMR and the SDEM models have to be calibrated to the measured core data. The permeability estimations using the SDEM model have a comparable uncertainty to that of standard NMR permeability models. This work introduces the use of SDEM models applied in conjunction with the T-S plot for the estimation of permeability. This allows geology-based models incorporating the differing length scales of the clays to be built. Because the model performs as well as the NMR-based permeability models, the application of the SDEM model can result in significant financial savings. The use of the T-S plot means that varying N/G and volumes of dispersed clay are accounted for, giving increased accuracy and the ability to extrapolate the model.