Influence of recharge rates on steady-state plume lengths

doi:10.1016/j.jconhyd.2020.103709

Journal of Contaminant Hydrology

Volume 235, November 2020, 103709

https://doi.org/10.1016/j.jconhyd.2020.103709 Get rights and content

Highlights

•
Qualitative and quantitative impact of recharge rates on steady-state plume length.
•
Hybrid analytical- empirical solution for estimation of steady-state plume lengths with recharge.
•
Confirmation with a selection of field data of contamination sites.

Abstract

A large number of potentially contaminated sites reported worldwide require cost- and time-effective assessment of the extent of contamination and the threats posed to the water resources. A significant risk assessment metric for these sites can be the determination of the maximum (i.e., steady-state) contaminant plume length (L_max). Analytical approaches in the literature provide an option for such an assessment, but they include a certain degree of uncertainty. Often, the causes of such uncertainties are the simplifications in the analytical models, e.g., not considering the influence of hydrogeological stresses such as recharge, which impact the plume development significantly. This may lead to an over- or underestimation of L_max. This work includes the influence of the recharge for the effective estimation of L_max. For that, several two-dimensional (2D) numerical simulations have been performed by considering different aquifer thicknesses (1 m– 4 m) and recharge rates (ranging from 0 to 3.6 mm/day). From the numerical results of this work, it has been deduced that 1) the application of the recharge shortens L_max, and the recharge entering the aquifer top causes the plume to tilt, 2) the reduction percentage in L_max depends on the recharge rate applied and the aquifer thickness, and 3) the reduction percentage varies in a non-linear manner with respect to the recharge rate for a fixed aquifer thickness.

Based on these results, a hybrid analytical-empirical solution has been developed for the estimation of L_max with the inclusion of the recharge rate. The proposed hybrid analytical-empirical solution superimposes an empirically obtained correction factor onto an analytical solution. Although extensive confirmation steps of the developed model are required for including the effect of the recharge on aquifer hydraulics, the proposed expression improves the estimation of the L_max significantly. The hybrid analytical-empirical solution has also been confirmed with a selection of limited field contamination sites data. The hybrid model result (L_hyb) provides a significant improvement in the estimation, i.e., an order of magnitude lower mean relative error compared to the analytical model.

Introduction

Water stress is emerging as one of the major global issues. Schlosser et al. (2014) stated that by the year 2050, 52% of the population worldwide might be living under at least moderately stressed water resource conditions, and one-fifth of it might be living in regions with over-exploited water resources. Worldwide, 2.5 billion people are dependent on groundwater to fulfill their basic daily water needs (WWAP, 2012). Unlike the surface water resources, which are accessible at limited locations only, groundwater is easily available in many places. Hence, it forms the largest share of the world's agriculture and drinking water supply. Additionally, it is also a source of the base flow of surface water systems. Therefore, deterioration in the quality of the groundwater may also affect the quality of the surface water, which forms a significant source of supply as well.

The cumulative effect of groundwater contamination poses a serious threat to water resources, associated ecosystems, and drinking water security. Therefore, there is a pressing need for studies concerning the assessment and remediation of the contaminated sites. As per the EEA (2014), approximately 14% of an estimated 2.5 million potentially contaminated sites in the European Union (EU) are expected to be contaminated and in need of remediation. While one-third of these contaminated sites have been identified already, only about 15% have been remediated so far (EEA, 2014). Given the immense size of the problem, effective assessment and management techniques are required. EEA (2014) suggested that the cost of remediation could be over ten times the investigation cost (40% of the reported cases). Thus, it is essential to gauge the magnitude of the problem in order to assess the required resources like workforce, finances, and time (EEA, 2014).

There have been numerous research works on contaminant transport and plume development over the decades. Bear (1979) and Batu, 1989, Batu, 2005 discussed the development of analytical models for the estimation of natural attenuation. Zhang et al., 2007, Zhang et al., 2008 conducted physical experiments to examine groundwater flow and contaminant spreading in the subsurface to support the development of mathematical models. Field studies by Conant Jr et al. (2004) investigated the influence of contaminant plumes on local streams, ponds, and rivers. Also, Ham et al. (2004), Chu et al. (2005), Liedl et al., 2005, Liedl et al., 2011, and Cirpka et al. (2006) proposed analytical solutions for estimating the steady-state (or maximum) plume length (L_max) based on several assumptions such as homogeneous two-dimensional aquifer domain, uniform flow, and straightforward reaction mechanisms. Likewise, Maier and Grathwohl (2006) developed an empirical method for calculating the L_max through a large number of numerical simulations. Furthermore, the architecture of a source zone was studied through non-invasive imaging by Werth et al. (2010). de Barros and Nowak (2010) introduced the concept of effective source width and source efficiency and their importance in assessment of plume developemnt. Furthermore, Cirpka et al. (2012) discussed the steady-state reactive transport in two-dimensional heterogeneous porous media to quatfy the sources of uncertainity in predicting contaminant plume lengths.

Preliminary investigations using field exploration techniques and laboratory experiments are conventionally used for site management. However, considering a large number of potentially contaminated sites, they may prove to be challenging as well as very expensive. Numerical models provide a better alternative over the field methods, and they are widely prevalent. However, they too prove to be intractable due to the requirements of extensive data pertaining to the aquifer, contaminants, and technical expertise. In such cases, analytical solutions or empirical models can provide a satisfactory alternative to preliminary investigations, given the availability of minimal data-input required.

Determining a reasonably good estimate of L_max, which mostly represents a worst-case scenario, can serve as an adequate measure for the pre-assessment of a contaminant site. As such, analytical or empirical models can be advantageous for predicting L_max with the input of very few parameters. However, the available models (e.g., Ham et al., 2004; Liedl et al., 2005, Liedl et al., 2011; Cirpka et al., 2006; Cirpka and Valocchi, 2007; Maier and Grathwohl, 2006) often oversimplify the real site conditions thus quite often leading to a highly overestimated or underestimated value of L_max. Therefore, in the current state, the available analytical solutions have limited field applicability owing to the complex scenarios at real sites. A large number of contaminated sites, huge costs involved in field investigation techniques, and difficulties associated with the numerical models indicate the research gap in the development of analytical/empirical models beyond the simplifying assumptions.

A few research works have tried to assess the performance of analytical solutions beyond the simplifying assumptions, e.g., Yadav et al. (2013) investigated the impact of partially penetrating contamination sources on L_max based on the scenarios presented in Liedl et al., 2005, Liedl et al., 2011 for several 2D and 3D cases. Other works, e.g., Yang et al. (2012) and Jeon et al. (2013) suggested that hydrogeological stresses (external stresses) like seasonal hydrologic variations, flood events, groundwater abstraction, irrigation or drainage, precipitation, and lake stage variation influence the contaminant transport. Yang et al. (2012) found a strong correlation between the contaminant concentration levels in the groundwater with seasonal recharge and the fluctuations in groundwater levels. The contaminant concentrations and the solute mass discharge through the source were also found to be closely associated with the seasonal recharge and the changes in the groundwater table levels. Jeon et al. (2013) also found a close association between the groundwater levels and the levels of contaminant concentration, indicating an increase in the concentration during the dry season. This showed the likely impact of change in groundwater levels on the fate and transport of contaminants. The long-running residence time of contaminants (e.g., NAPLs) in the subsurface also makes the external stresses a critical factor.

Furthermore, the extreme cases of external stresses, such as floods, droughts, and pumping, may impact the plume development significantly. The direction and volume of contaminant flux respond to the changes in the groundwater levels originating from these external stresses. The above discussion on the current state of steady-state models and the influence of external stresses on L_max identifies a shortcoming in the ability of analytical models for a proper assessment of the contaminated sites under the influence of external stresses.

The motivation behind this study is to investigate the influence of recharge rates on the steady-state plume length by applying a numerical approach, i.e., finite difference scheme, and the development of a novel hybrid analytical-empirical solution for the subsurface transport problems. For this work, a hybrid analytical-empirical solution (referred to as “hybrid model” hereafter) is defined as one which is developed by the superimposition of analytical model and empirical model. The innovative hybrid model is presented, providing a relationship between L_max and recharge rate, with all the other assumptions still valid, as stated in the analytical development of L_max by Liedl et al. (2005). The proposed hybrid model is then evaluated against a set of selected field plume lengths. As the focus of the work is on the development of a hybrid model, the selection of the analytical model is still based on simple assumptions. More precisely, the base analytical model (Liedl et al., 2005) provides a vertically oriented two-dimensional model that may suit best for the application of a vertical recharge process. The selection of a more robust base analytical models is an interesting direction of research, and it will be treated in future work.

The work is organized in the following order: First, the conceptual geometry with the underlying hydro-geophysical state is presented. This is followed by introducing a numerical scheme that allows the use of a conservative model to simulate a reactive system. In the second step, the numerical results are presented. The development of the hybrid model is presented in the third step, which is followed by the evaluation of the proposed model as the final step.

Section snippets

The conceptual model

The domain for the numerical modeling (see Fig. 1) has been set in a manner similar to the conceptual model proposed by Liedl et al. (2005). To the best of the authors' knowledge, the solution given by Liedl et al. (2005) is the only two-dimensional analytical solution that considers a vertical aquifer cross-section. Such a conceptual model provides a better representation of the supply of electron acceptor (EA) and the recharge entering the aquifer from the top boundary in comparison to

Steady-state plume length under the influence of recharge rates

The base model results have been considered well- confirmed, as, without the application of recharge, the numerical plume lengths provided a close match (up to 95% accurate) to analytical plume lengths. Once confirmed, the simulations have been performed with the application of recharge. The results have suggested the downward diversion and decreased longitudinal extension of the plumes on the application of the recharge (see Fig. 4(a)). The recharge entering the aquifer causes the plume to

Conclusions

The current study proposes an innovative approach for evaluating the steady-state plume lengths with the inclusion of the influence of the recharge rates. A two-dimensional numerical model similar to the conceptual model from Liedl et al. (2005) has been set up with a homogeneous aquifer domain, uniform flow field, and instantaneous bi-molecular reaction mechanism. Simulations have been run for different values of the recharge rates to determine the influence of the recharge rates on the

Author statement

Sandhya Birla: Conceptualization, Data Curation, Investigation, Formal analysis, Visulatization, Validation, Writing - original draft, Writing - review & editing.

Prabhas Kumar Yadav: Methodology, Funding acquisition, Conceptualization, Writing – original draft, Writing - review & editing, Project administration, Supervision.

Poornima Mahalawat: Investigation, Formal analysis, Visualization.

Falk Händel: Conceptualization, Methodology, Project administration, Writing - review & editing,

Declaration of Competing Interest

None.

Acknowledgments

The authors would like to acknowledge the DAAD (German Academic Exchange Service) for supporting this work. The authors would also like to thank the German Research Foundation (DFG) for financial support through the research grant ESTIMATE (LI 727/29-1) and (DI 833/22-1).

References (29)

F.P. de Barros et al.
On the link between contaminant source release conditions and plume prediction uncertainty
J. Contam. Hydrol.
(2010)
O.A. Cirpka et al.
Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state
Adv. Water Resour.
(2007)
O.A. Cirpka et al.
Stochastic evaluation of mixing-controlled steady-state plume lengths in two-dimensional heterogeneous domains
J. Contam. Hydrol.
(2012)
B. Conant et al.
A PCE groundwater plume discharging to a river: influence of the streambed and near-river zone on contaminant distributions
J. Contam. Hydrol.
(2004)
P.A. Ham et al.
Effects of hydrodynamic dispersion on plume lengths for instantaneous bimolecular reactions
Adv. Water Resour.
(2004)
U. Maier et al.
Numerical experiments and field results on the size of steady state plumes
J. Contam. Hydrol.
(2006)
C.J. Werth et al.
A review of non-invasive imaging methods and applications in contaminant hydrogeology research
J. Contam. Hydrol.
(2010)
C. Zhang et al.
Evaluation of simplified mass transfer models to simulate the impacts of source zone architecture on nonaqueous phase liquid dissolution in heterogeneous porous media
J. Contam. Hydrolo.
(2008)
R.C. Acharya et al.
Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional porous media
Water Resour. Res.
(2007)
V. Batu
A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type boundary condition at the source
Water Resour. Res.
(1989)

V. Batu

Applied Flow and Solute Transport Modeling in Aquifers: Fundamental Principles and Analytical and Numerical Methods

(2005)

J. Bear

Hydraulics of Groundwater

(1979)

M. Chu et al.

Modeling microbial reactions at the plume fringe subject to transverse mixing in porous media: when can the rates of microbial reaction be assumed to be instantaneous?

Water Resour. Res.

(2005)

O.A. Cirpka et al.

Determination of transverse dispersion coefficients from reactive plume lengths

Groundwater

(2006)

Cited by (7)

A data-driven approach for simplifying the estimation of time for contaminant plumes to reach their maximum extent
2024, Journal of Contaminant Hydrology
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 $T = T_{Lmax}$ , at which the plume reaches its maximum extent $L = L_{\max}$ . An approach to easily obtain an estimate of $T_{Lmax}$ in particular is presented in this work. Limited availability of high-quality field data, particularly of $T_{Lmax}$ , 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 $T_{Lmax}$ . 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 $(λ_{EFF})$ and at the source $(γ)$ as dominantly most influential for $T_{Lmax}$ . For $L_{\max}$ , the first-order decay rate constant $λ_{EFF}$ and groundwater velocity $v$ are the two important parameters. The sensitivity analysis also identifies that these parameters non-linearly impact $T_{Lmax}$ or $L_{\max}$ . With this information, the proposed polynomial models (each for $L_{\max}$ and $T_{Lmax}$ ) 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 $T_{Lmax}$ , for which only very limited field or literature information is available.
Direct computation of critical plume quantities required for initial assessment of contaminated sites
2023, Computers and Geosciences
Estimates of plume extremes such as maximum plume width ( $W_{m a x}$ ) and its location ( $X_{w m a x}$ ), maximum plume area ( $A_{m a x}$ ), and maximum plume length ( $L_{m a x}$ ), which are vital indicators of any site assessment work, mostly requires the use of rather complicated numerical approaches and a large number of site information. This paper focuses on simpler (semi)analytical quantification of $W_{m a x}$ and $X_{w m a x}$ , and their characterization with respect to source geometry (source width $S_{w}$ and source thickness $S_{t}$ ) for estimating $A_{m a x}$ . A direct computation of $W_{m a x}$ and $X_{w m a x}$ rather becomes a multi-dimensional nonlinear system problem for which only a few iterative methods are available. The challenge magnifies further as limited information on $W_{m a x}$ and $X_{w m a x}$ are available for obtaining an initial guess of the solution. Solving over 1000 synthetic problems, this work finds the Newton–Krylov method as the most suitable nonlinear system solver. Among the most important were the limiting results such as $L_{m a x}$ /8 ¡ $X_{w m a x}$ ¡ $L_{m a x}$ /8 and $1 \times S_{w}$ ¡ $W_{m a x}$ ¡ $1.4 \times S_{w}$ . These limiting results simplify the finding of initial guesses for $W_{m a x}$ and $X_{w m a x}$ . Further characterization of $W_{m a x}$ and $X_{w m a x}$ with $L_{m a x}$ , $S_{t}$ , and $S_{w}$ provided an empirical relation between plume and source areas, in addition to an approximation of $A_{m a x}$ . A field site data illustrate the potential applications of the methods developed in this work.
An approach for quantification of the heterogeneity of DNAPL source zone geometries
2022, Journal of Contaminant Hydrology
Citation Excerpt :
When field contamination scenarios are predicted, simplified SZ structures with simple geometrical shape (line or rectangle) including also simplified domain (uniform flow and aquifer parameters) are often used in the models (Domenico, 1987; Liedl et al., 2005, 2011; Chu et al., 2005; Maier and Grathwohl, 2006; Karanovic et al., 2007 etc.). The use of simplified SZ structures decreases the accuracy of model prediction (Birla et al., 2020; Engelmann et al., 2019a). To the authors' best knowledge, a detailed quantification method of the real-life SZ shape is not yet available, which relies on direct estimation of the shape dimensions rather than inverse methods.
Many studies have investigated the migration and entrapment processes of source zones from dense non-aqueous phase liquid (DNAPL) contamination under different conditions. However, the characterization of occupying area by source zone (or source shape) in water-saturated aquifers is still rudimentarily considered. In this study, we demonstrated this issue (1) by providing a brief review of existing approaches for source shape consideration, (2) by proposing an approach with simple shape parameters based on the non-uniformity of source widths, and (3) by providing exemplary applications of our proposed approach on shapes already published in previous research works. Our literature review suggested that the source zone in mathematical approaches is generally characterized as simple geometrical shapes (arbitrary lines or rectangles) or system-defined parameters that contrast to complex and discontinuous shapes observed in the real world. But the characterization of such complex shapes is still not possible with acceptable efforts. Therefore, we proposed an approach to parameterize the source shape by considering the variation of width and midpoints over the depth of the entire source zone and formulate four parameters based on population statistics (mean, standard deviation). To illustrate the suitability of our approach, we applied it to the results of lab experiments, and by analyzing these complex shapes, we highlighted the potential for improving the characterization techniques of non-uniformity of the source zones.
Regional modeling of groundwater recharge in the Basin of Mexico: new insights from satellite observations and global data sources
2023, Hydrogeology Journal
A 3D hybrid model for estimation of steady-state plume lengths with the influence of recharge
2023, Environmental Earth Sciences
Contamination Assessment and Site-Management Tool (CAST): A Browser-Based Tool for Site Assessment
2022, Groundwater

View all citing articles on Scopus

View full text

Influence of recharge rates on steady-state plume lengths

Highlights

Abstract

Introduction

Section snippets

The conceptual model

Steady-state plume length under the influence of recharge rates

Conclusions

Author statement

Declaration of Competing Interest

Acknowledgments

J. Contam. Hydrol.

Adv. Water Resour.

J. Contam. Hydrol.

J. Contam. Hydrol.

Adv. Water Resour.

J. Contam. Hydrol.

J. Contam. Hydrol.

J. Contam. Hydrolo.

Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional porous media

Water Resour. Res.

A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type boundary condition at the source

Water Resour. Res.

Applied Flow and Solute Transport Modeling in Aquifers: Fundamental Principles and Analytical and Numerical Methods

Hydraulics of Groundwater

Modeling microbial reactions at the plume fringe subject to transverse mixing in porous media: when can the rates of microbial reaction be assumed to be instantaneous?

Water Resour. Res.

Determination of transverse dispersion coefficients from reactive plume lengths

Groundwater