Analysis of the fate and transport of nC₆₀ nanoparticles in the subsurface using response surface methodology

Predicting the distribution of engineered nanomaterials (ENMs) in the environment will provide critical information for risk assessment and policy development to regulate these emerging contaminants. The fate and transport of ENMs in natural subsurface environments are complicated by various factors, such as hydraulic gradient, initial release concentration, nanoparticle size, and collision efficiency factor. Based on advanced statistical methodologies (i.e., response surface methodology (RSM)), we explore simple relationships between key factors that control ENM transport (collision efficiency factor, particle size, hydraulic gradient, and initial release concentration) and key parameters that describe the ENM concentration distribution in porous media (maximum standardized concentration, the mass percentage of injected nanoparticle attached in the aquifer, the x-centroid of aqueous phase nC₆₀ plume, and the x-centroid of attached phase nC₆₀ distribution). Hypothetical scenarios for the release of nanoparticles into an aquifer were simulated numerically with randomly generated permeability fields that were based on mildly and highly heterogeneous sites. RSM was used to develop polynomial regression equations based on a statistical experimental design. High R-squared values (greater than 0.9) of the regression equations were obtained for all the models developed based on the mildly heterogeneous site. On the highly heterogeneous site, the R-squared value of the regression equation for the percentage of nanoparticles attached (by mass) was more than 0.9. The ability to accurately estimate aqueous phase ENM concentration distribution using simple regression equations is particularly critical for risk assessment. Even though the correlations developed in this study were site and scenario specific, this work represents a first effort of applying RSM for predicting the distribution of engineered nanomaterials in porous media.