Tom Bultreys , Kamaljit Singh, Ali Q. Raeini, Leonardo C. Ruspini, Pål-Eric Øren, Steffen Berg, Maja Rücker , Branko Bijeljic, Martin J Blunt 

At the pore scale, slow invasion of a wetting fluid in porous materials is often modelled with quasi-static approximations which only consider capillary forces in the form of simple pore filling rules. The appropriateness of this approximation, often applied in pore network models, is contested in literature, reflecting the difficulty of predicting imbibition relative permeability with these models. However, validation by sole comparison to continuum-scale experiments is prone to induce model overfitting. It has therefore remained unclear whether difficulties generalizing the model performance are due to network extraction, the pore filling rules, or whether a quasi-static description is useful at all. Here, we address this by examining whether such a model can predict the pore-scale fluid distributions underlying the behaviour at the continuum scale. To this end, we compare the fluid arrangement evolution measured in fast synchrotron micro-CT experiments on two rock types to quasi-static simulations which implement capillary-dominated pore filling and snap-off, including a sophisticated model for cooperative pore filling. The results indicate that pore network models with appropriate pore filling rules can in principle obtain a good first-order prediction of the upscaled flow properties of strongly-wetted rocks at low capillary numbers.