Mathematical modeling the transport of few-layer graphene in saturated porous media

Abstract

This mathematical modeling study incorporates an existing set of effluent data for FLG-NPs transport through water-saturated quartz sand to estimate kinetic particle mobility parameters for a range of experimental ionic strengths (IS) and organic macromolecules (OMs) concentrations. Parameter estimation was done by implementing several NP filtration models in inverse analyses: (i) the clean-bed colloid filtration theory model (CFT, ii) maximum retention capacity model (MRC), and (iii) two subclasses of a two-attachment-site model (2S). It was found that as solution IS (1-100 mM NaCl) increased, the kinetic conditions for particle-collector attachment transitioned from unfavorable (i.e. fractional attachment) to favorable (i.e. diffusion-limited), and the unbounded subclass of 2S lost the better numerical performance compared to CFT and MRC; as the difference between the normalized sum of squared residuals (NSSR) of the unbounded subclass of 2S and CFT decreased from 20% at 1 mM to less than 1% at 100 mM NaCl suggesting the adequacy of CFT to estimate mobility parameters at high ionic strength.As the OMs concentrations increased from 0.8 to 50 total organic carbon (mg (TOC)/L) in the system, the unbounded subclass of 2S showed the best outcomes. Simulation results from all models predicted that attachment efficiency decreases with increasing OM concentration consistent with the observed enhancement of FLG mobility at higher OM levels. The FLG detachment rate coefficient slightly increased with an increase of OM concentration in the influent. The unbounded four-parameter subclass of 2S exhibited a numerical advantage in comparison with CFT and MRC models for estimating FLG mobility parameters at low IS (1 mM NaCl) and high OMs concentration (50 mg (TOC)/L). However, the CFT model yielded similar goodness of fit values very similar to 2S and MRC models at high IS (100 mM NaCl) and low OMs concentration (0.8 mg (TOC)/L).