A data-driven approach for simplifying the estimation of time for contaminant plumes to reach their maximum extent

Abstract

Globally there exist a very large number of contaminated or possibly contaminated sites where a basic preliminary assessment has not been completed. This is largely, among others, due to limited simple methods/models available for estimating key site quantities such as the maximum plume length, further denoted as $L_{\max }$ and the corresponding time $T=T_{\mathrm{Lmax}}$, at which the plume reaches its maximum extent $L=L_{\max }$. An approach to easily obtain an estimate of $T_{\mathrm{Lmax}}$ in particular is presented in this work. Limited availability of high-quality field data, particularly of $T_{\mathrm{Lmax}}$, necessitates the use of synthetic data, which constrains the overall model development works. Taking BIOSCREEN-AT (transient 3D model) as a base model, this work proposes second-order polynomial models, with only two parameters, for estimating $L_{\max }$ and $T_{\mathrm{Lmax}}$. This reformulation of the well established solution significantly reduces data requirement and workload for initial site assessment purposes. A global sensitivity analysis (Morris, 1991), using a large number of random synthetic data, identifies the first-order decay rate constants in the plume $\left({\lambda }_{\mathrm{EFF}}\right)$ and at the source $\left(\gamma \right)$ as dominantly most influential for $T_{\mathrm{Lmax}}$. For $L_{\max }$, the first-order decay rate constant ${\lambda }_{\mathrm{EFF}}$ and groundwater velocity $v$ are the two important parameters. The sensitivity analysis also identifies that these parameters non-linearly impact $T_{\mathrm{Lmax}}$ or $L_{\max }$. With this information, the proposed polynomial models (each for $L_{\max }$ and $T_{\mathrm{Lmax}}$) were trained to obtain model coefficients, using a large amount of synthetic data. For verification, the developed models were tested using four datasets comprising over 100 sample sets against the results obtained from BIOSCREEN-AT and the developed BIOSCREEN-AT-based steady-state model. Additionally, the developed models were evaluated against two well documented field sites. The proposed models largely simplify estimation, particularly, of $T_{\mathrm{Lmax}}$, for which only very limited field or literature information is available.