Critical Assessment of Models for Transport of Engineered Nanoparticles in Saturated Porous Media

Abstract

To reliably assess the fate of engineered nanoparticles (ENP) in soil, it is important to understand the performance of models employed to predict vertical ENP transport. We assess the ability of seven routinely employed particle transport models (PTMs) to simulate hyperexponential (HE), nonmonotonic (NM), linearly decreasing (LD), and monotonically increasing (MI) retention profiles (RPs) and the corresponding breakthrough curves (BTCs) from soil column experiments with ENPs. Several important observations are noted. First, more complex PTMs do not necessarily perform better than simpler PTMs. To avoid applying overparameterized PTMs, multiple PTMs should be applied and the best model selected. Second, application of the selected models to simulate NM and MI profiles results in poor model performance. Third, the selected models can well-approximate LD profiles. However, because the models cannot explicitly generate LD retention, these models have low predictive power to simulate the behavior of ENPs that present LD profiles. Fourth, a term for blocking can often be accounted for by parameter variation in models that do not explicitly include a term for blocking. We recommend that model performance be analyzed for RPs and BTCs separately; simultaneous fitting to the RP and BTC should be performed only under conditions where sufficient parameter validation is possible to justify the selection of a particular model.

Retention of Nanoparticles: From Laboratory Cores to Outcrop Scale

“…This behavior of NPs has been shown to be captured by the two-site retention model [46] and has also been shown to work better than the other retention models that simulate NP retention. Some of those models were also reviewed by Goldberg et al [49], whose findings confirm with the study of Zhang et al [46]. The other retention models that have been used in the past include (i) the colloid filtration model, (ii) filtration model with site blocking, (iii) filtration model with detachment, and (iv) kinetic Langmuir model.…”

Transport and Retention of Polyvinylpyrrolidone‐Coated Silver Nanoparticles in Natural Soils

“…In this study, some RPs of the PVP‐AgNPs in the RS were nonmonotonic with depth and the one‐site kinetic retention model described above did not account for the nonmonotonic RPs. While a complex transport model, i.e., the two‐species model that includes two different species among colloid populations with two different deposition rates, can well approximate the nonmonotonic RPs (see Supplemental Material S2 for details), a large number of parameters ( n ≥ 6) need to be fitted simultaneously and the model‐fitted transport parameters do not necessarily provide insights into the transport behavior of colloids and NPs in porous media, especially for highly complex and heterogeneous natural soils (Goldberg et al, 2014). Consequently, in this work, we selected a simple one‐site kinetic retention model to simulate the PVP‐AgNP BTCs alone to compare the intrinsic transport mechanisms of the PVP‐AgNPs in the soils by avoiding overparameterization.…”

Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

“…Breakthrough curves are curves of concentrations measured at an observation point downstream from a source plotted against time. Least square regression methods are generally used for fitting breakthrough curves of column experiments and tracer tests with subsurface transport models [84][85][86][87][88][89][90][91][92][93][94][95][96]. Subsequently, model weight calculation and ranking of multiple candidate models are carried out using an approximate semi-analytical solution [85,87], which indirectly accounts for model complexity as previously discussed.…”