Modeling graphene oxide transport and retention in biochar

Experimental data from fixed-bed column studies and a numerical model based on convection-dispersion equations were used to describe transport and retention of Graphene Oxide (GO) in sand, biochar (BC), and BC modified with nanoscale zero-valent iron (BC-nZVI). Three blocking functions, namely no blocking, site-blocking, and depth-dependent blocking, were used to analyze GO transport and retention behavior in each media as a function of Ionic Strength (IS). An inverse modeling approach was implemented to determine the attachment coefficient (K_a) and maximum solid-phase retention capacity (S_max). The Langmuirian attachment model with site-blocking function effectively described experimental GO breakthrough curves (R² ~ 0.70-0.99) compared to other models, indicating the importance of introducing a limit on the attachment capacity of the media. The K_a values for BC and BC-nZVI were significantly higher than sand, attributable to high porosity, roughness, and surface chemical properties. The models predicted an increasing trend in K_a (0.065 to 0.615 min^-1) in BC with increasing IS (0.1 to 10 mM), while K_a values decreased (2.26 to 0.349 min^-1) for BC-nZVI. A consistent increase in S_max was observed for both BC and BC-nZVI with increasing IS. Scenario analysis was conducted to further understand the effect of influent IS, GO concentration, and treatment depth. BC-nZVI exhibited a higher K_a and S_max and as a result, higher GO retention than BC at lower IS (0.1 and 1.0 mM). BC-nZVI had a relatively lower K_a (0.349 min^-1) at 10 mM IS, however, it outperformed BC when GO retention capacities are compared over a longer period attributable to a higher S_max (6.47). Complete GO breakthrough occurred in a 5 cm media after 350 and 465 days for BC and BC-nZVI, respectively at 10 mM IS and influent concentration of 0.1 mg·L^-1. GO breakthrough time increased with increasing treatment depth, however, the relation was non-linear.