Modeling Oil Recovery for Mixed Macro- and Micro-Pore Carbonate Grainstones

In general, modeling oil-recovery is a challenging problem involving detailed fluid flow calculations with required structural details that challenge current experimental resolution. Recent laboratory experiments on mixed micro- and macro-pore suggest that there is a systematic relationship between remaining oil saturation (ROS) and the fraction of micro-pores. Working with experimental measurements of the pores obtained from X-ray tomography and mercury intrusion capillary pressure porosimetry, we define a digital rock model exemplifying the key structural elements of these carbonate grainstones. We then test two fluid-flow models: invasion percolation model and effective medium model. Although invasion percolation identifies the important impact of macro-pore percolation on permeability, it does not describe the dependence of ROS on micro-pore percentage. We thus modified the effective medium model by introducing a single-parameter descriptor, r_eff. Oil from pores r ≥ r_eff is fully removed, while for the remaining pores with r < r_eff, their contribution is scaled by (r/r_eff)². Applying this straightforward physics to pore size distributions for the mixed-pore grainstones reproduces the experimental ROS dependence.