Two-Step Upscaling of Sub-Seismic Geo-Heterogeneity with Flow-Rate-And Direction Dependent Saturation Functions

Saturation distributions that ensue when supercritical CO₂ is injected into heterogeneous porous sedimentary rocks depend on the local balance between viscous, gravitational, and capillary forces. This balance varies among different constituent rock types, and there is mounting evidence that this variation needs to be accounted for when modelling relative permeability and capillary pressure between capillary (CL) and viscous limit (VL) two-phase flow. Here we present field data-based numeric-simulation research upscaling such novel rate-dependent, directional functions to the permeability REV of the sedimentary rock to determine the injection behaviour of the fluvio-deltaic Parraatte formation at the CO2CRC's Otway International Test Centre, Australia. The flow of CO₂-water along a high-resolution (0.05 m 1 m) vertical cross-section between two wells, spaced 640 meters apart is simulated and upscaled in two stages. The passage of the saturation front through the studied cross-section is analyzed for different line-drive rates, and dynamic drainage relative permeability curves are measured in REV scale sampling windows placed at different locations on the cross section. This analysis delivers full tensor-type dynamic relative permeability curves also accounting for buoyancy-driven flow. These REV scale functions are the macroscopic expression of unstable displacement, and heterogeneity-induced fingering of the CO₂ phase, diminishing sweep and promoting early breakthrough at average saturations of 5-15%. The practical importance and workflow implications of these rate-dependent, tensorial saturation functions are explored.