Simulation of Immiscible Counter-Current Flow in Porous Media Using a Modified Dynamic Pore Network Model

Accurately simulating immiscible counter-current flow is crucial for applications from geological CO2 storage to shale gas production, yet it remains a major challenge for conventional pore network models (PNMs), which are unable to handle the numerical instability of opposing flows. To address this critical gap, we developed a novel dynamic PNM that incorporates a ‘transition state’ algorithm. This method successfully eliminates the spurious meniscus oscillations that hinder traditional models, enabling robust simulation of the complete counter-current process. Using this model, we quantify the profound impact of pore structure on flow efficiency. Our results demonstrate that increasing the pore size distribution uniformity (Weibull shape factor k from 0.5 to 3.0) extends the persistence of continuous air outflow pathways by more than six-fold (from 359 to over 2300 simulation steps). This leads to a quantifiable increase in the initial fluid exchange rate by nearly 10 times (from 10−11 to 10−10 m3/s) and a reduction in final residual air saturation by 53% (from 0.91 to 0.43). This work provides a tool for predicting and optimizing counter-current flow efficiency in subsurface engineering applications.