Continuum vs macroscopic invasion percolation models: a practical guide for choosing an appropriate model

The computational cost of continuum Darcy-based models in two-phase flow simulations has led to the introduction of simpler and faster approaches such as macroscopic invasion percolation (MIP). However, neglecting viscous forces limits the applicability of MIP and can result in inaccurate results if used under unsuitable conditions. The results of this study challenge the commonly accepted belief that the existence of negligible viscous forces is both necessary and sufficient to justify the use of MIP models. This study offers concrete model selection criteria by comparing the results of a continuum (CompSim) and an MIP-based model (ET-MIP) in simulating air sparging into a two-dimensional domain over a range of capillary numbers (Ca). The effects of air injection rate (Q_a), soil permeability (k), and soil heterogeneity (SDlnk) were studied. The Q_a range was designed to produce Ca < 10^-4, which is common in different applications, such as air sparging, CO₂ storage, and electrical resistance heating. Jaccard coefficient (J) was used to compare the predicted gas flow pathways of the two models. The accuracy of MIP declined with injection rate while its applicability extended up to Ca ≈ 1.16 × 10^-6 for a more heterogeneous soil (SDlnk = 1). The results demonstrated that a sufficient level of soil heterogeneity is essential for MIP to be reliable. Equivalent heterogeneity lengths (h_eq,gr and h_eq,visc) were introduced as surrogates for heterogeneity to allow for scaling of heterogeneity between different soils and for different pairs of fluids, and a phase diagram was designed based on h_eq,gr and heq_,visc. The diagram was divided into three regions of Zone 1: MIP recommended, Zone 2: MIP misses some side branches, and Zone 3: MIP not recommended. This diagram can be used to quickly decide if an application should use continuum modelling or if an MIP model is sufficient.