Colloid filtration prediction by mapping the correlation-equation parameters from transport experiments in porous media

Colloid filtration theory (CFT) is a conceptual construct for predicting the characteristic rate of colloid-surface collisions during transport in granular porous media. A central product of this theory is the correlation equation for predicting collection-efficiency (eta), based exclusively on theoretical model development. Specifically, the eta-equation has terms combining dimensionless groups (of physicochemical properties) with unknown parameters that are usually fitted so that the predicted eta matches that determined by colloid-surface collisions simulated in idealized pore-scale models. In this study, we replace the simulated colloid-surface collisions in idealized models with experimental column-scale data on apparent colloid-surface collisions. A new correlation equation is obtained by minimizing the difference between eta determined by the correlation equation and that determined experimentally, using data from a collection of experiments for favorable conditions for colloid filtration. In this way, we parameterize a mechanistically based eta-equation with empirical evidence. The impact of different properties of colloids and porous media is studied by comparing experimental properties with different terms of the correlation equation. This comparison enables insight about the different processes that occur during colloid transport and retention in porous media, such as diffusion and interception, and provides directions for future CFT developments that will need to account for these processes differently than the current theory does. Additionally, we find that while most of the parameters of the presented eta-equation are only slightly different than those proposed in previous theoretical studies, the match between theory and observation is significantly improved. For the available experimental data, which provide a reasonable representation of property ranges for many applications of CFT, the proposed equation provides a closer match to the experimentally measured collection efficiencies compared to available theories to date.