Inversion-Based Thomas-Stieber Approach to Estimate Storage and Flow Properties of Heterogeneous Shaly Sandstones
Authors:   The University of Texas at Austin, Eghbali Ali , Torres-Verdin Carlos ,   The University of Texas at Austin, Acosta Elias R. ,   Staatsolie Maatschappij Suriname N.V.
Published: November 2024

We generalize the Thomas-Stieber (T-S) concept to develop an inversion-based interpretation method of well logs to estimate storage and flow properties of arbitrarily heterogenous sandstone-shale sedimentary sequences. Firstly, we use well logs to simultaneously estimate shale lamination volume, Vlam, and dispersed clay concentration, Vdisp. Estimation results are used to calculate storage and flow properties by implementing rock classification and rock-class-dependent petrophysical models. The general inversion-based T-S estimation method overcomes practically all the limitations of the standard T-S approach, such as (i) assuming the same properties for shale layers and grain-coating clay and (ii) T-S diagram axes (porosity-shale volume) are not readily available measurements. We also introduce a permeability model for arbitrary shaly sandstones that accounts for sandstone-shale laminations and dispersed clay. Permeabilities calculated parallel and perpendicular to the bedding plane are improved and successfully benchmarked against core measurements by combing the estimated Vlam and Vdisp. After establishing the forward model that relates Vlam and Vdisp to well logs, we minimize the squared difference between the available logs and their numerical simulations. The relationship between Vdisp, Vlam, and nuclear logs is nonlinear, while material balance must be honored in the estimation. Likewise, the choice of well logs for inversion, e.g., bulk density, gamma ray, or neutron, depends on their sensitivity to specific layer composition. Using an efficient gradient-based optimizer, we estimate Vlam and Vdisp and their uncertainty. When Vlam is not negligible, vertical and horizontal resistivity from triaxial induction become key measurements to assimilate electrical anisotropy in the estimations. Water-saturation models that account for the excess electrical conductivity of clay are invoked when Vdisp is nonzero. Next, we calculate the throat-radius reduction of a bundle of capillary tubes based on Vdisp. We also calculate the effect of sandstone-shale laminations on anisotropic flow properties. The resulting anisotropic permeability, verifiable against cores, is a function of shale-free sandstone, shale lamina, clay permeability endpoints, formation factor, Vlam, and Vdisp. When NMR data are available, predicted time-relaxation modalities should match the measurements. We verified the inversion-based interpretation workflow with two synthetic and one field case with core measurements. Inversion results decrease pore-volume errors by a factor of 3 compared to standard well-log analysis. Estimated permeabilities match core data within 2.6% on a logarithmic scale. We remark that rapid variations in the physical properties of clays/shales and rock composition require adjustments of the simulation endpoints. Nuclear logs are shallow-sensing measurements (only investigate the flushed zone), whereby the changes in input well logs are dominated by changes in Vlam and Vdisp. Depth-matching and borehole environmental effects are considered part of the inversion procedure. Results differentiate between pore-filling clays and laminated shales, while standard Thomas-Stieber-based well-log interpretation assumes the same endpoints for both. Furthermore, Thomas-Stieber methods assume a linear relationship between shale/clay volumes and nuclear logs that is inadequate and erroneous; they propagate measurement noise to interpretation results, while our inversion method mitigates instrument noise effects and explicitly accounts for the nonlinearity between measurements and estimated properties. Finally, there is no publication that relates the permeability of sandstone to permeability endpoints in thinly laminated, clayey-sandstone/shale sequences.