Multiscale Generalized Network Model Using Differential Micro-CT Imaging for Drainage in Heterogeneous Carbonates

Abstract Carbonate rocks exhibit complex pore structures with wide variability in size, shape and connectivity that challenge accurate multiphase flow modeling. While representing detailed throat geometry and fluid interfaces, the Generalized Network Model (GNM) overlooks sub-resolution porosity by relying on a single micro-CT (µCT) image. To address this limitation, we introduce the multiscale GNM that incorporates unresolved porosity regions using difference maps between dry and brine-saturated µCT images. These regions are simplified into Darcy-type microlinks that represent effective brine-invaded porosity while significantly reducing computational cost. The model is calibrated against mercury intrusion capillary pressure (MICP) and high-resolution differential imaging porous plate (DIPP) drainage data for heterogeneous Ketton and reservoir carbonate samples. Experimental data guide the tuning of model parameters to capture fluid invasion across different pore scales. Our findings highlight that sub-resolution porosity, particularly intermediate-sized pores, plays a key role in sustaining flow and connectivity, challenging the common assumption that unresolved pores are merely water-filled and poorly connected. The multiscale GNM reproduces experimental capillary pressure data and predicts water relative permeability with good quantitative accuracy in a blind test. This work provides a practical and efficient framework for reliable, physically grounded flow predictions in complex multiscale porous media, complementing costly, time-intensive laboratory measurements and reducing the reliance on often unavailable higher-resolution images.