Numerical modeling of contaminant transport in a stratified heterogeneous aquifer with dipping anisotropy

Abstract

The combined influence of dip angle and adsorption heterogeneity on solute transport mechanisms in heterogeneous media can be understood by performing simulations of steady-state flow and transient transport in a heterogeneous aquifer with dipping anisotropy. Reactive and non-reactive contaminant transport in various types of heterogeneous aquifer is studied by simulations. The hydraulic conductivity (K) of the heterogeneous aquifer is generated by HYDRO_GEN with a Gaussian correlation spectrum. By considering the heterogeneity of the adsorption distribution coefficient (K _d), a perfect negative correlation between lnK and lnK _d is obtained by using the spherical grains model. The generated K and K _d are used as input to groundwater flow and transport models to investigate the effects of dipping sedimentary heterogeneity on contaminant plume evolution. Simulation results showed that the magnitude of the dip angle strongly controls the plume evolution in the studied anisotropic and heterogeneous aquifer. The retarded average pore-water velocity (v/R) of the adsorption model significantly controls the horizontal spreading of the plume. The bottom plume is intensively retarded in the zones between the dipping lenses of lower hydraulic conductivity and the no-flow bottom boundary. The implications of these findings are very important for the management of contaminated heterogeneous aquifers.

Résumé

L’influence conjuguée de la valeur de la pente et de l’hétérogénéité de l’adsorption sur les mécanismes de transfert de soluté dans un aquifère hétérogène peut être appréhendée par la réalisation de simulations de l’écoulement permanent et du transfert transitoire dans un aquifère hétérogène à anisotropie de pendage. Le transfert de pollutant réactif et non réactif dans divers types d’aquifères hétérogènes est étudié grâce à ces simulations. La conductivité hydraulique (K) de l’aquifère hétérogène est générée par HYDRO GEN avec spectre de corrélation gaussien. En considérant l’hétérogénéité du coefficient de distribution de l’adsorption (K _d ), on obtient une corrélation négative parfaite entre lnK et lnK _d en utilisant le modèle des grains sphériques. Le K et le Kd générés sont utilisés comme entrées des modèles d’écoulement souterrain et de transfert, pour explorer les effets de l’hétérogénéité de l’inclinaison des couches sur l’évolution du panache de polluant. Les résultats de la simulation ont montré que la valeur de la pente influence fortement l’évolution du panache dans l’aquifère anisotrope et hétérogène étudié. La vitesse retardée moyenne de l’eau des pores (v/R) du modèle d’adsorption contrôle significativement l’extension horizontale du panache. Le panache de fond est retardé de manière intensive dans les zones entre les lentilles inclinées de plus faible conductivité hydraulique et la limite inférieure privée d’écoulement. Les implications de ces constats sont très importantes pour la gestion des aquifères hétérogènes contaminés.

Resumen

La influencia combinada del ángulo de inclinación y la heterogeneidad de la adsorción sobre los mecanismos de transporte de soluto en medios heterogéneos pueden ser entendida llevando a cabo simulaciones de flujo en estado estacionario y transporte transitorio en una acuífero heterogéneo con una anisotropía en la inclinación. Se estudiaron por simulaciones el transporte de contaminantes reactivos y no reactivos en varios tipos de acuíferos heterogéneos. La conductividad hidráulica (K) de un acuífero heterogéneo está generada por HYDRO_GEN con un espectro de Gausiano de correlación. Considerando una heterogeneidad del coeficiente de distribución de adsorción (K _d ), se obtuvo una correlación negativa perfecta entre lnK y lnK _d usando el modelo de granos esféricos. Los K y K _d generados son usados como entrada al modelo de flujo de agua subterránea y de transporte para investigar los efectos de la heterogeneidad sedimentaria inclinada sobre la evolución de la pluma de contaminantes. Los resultados de la simulación mostraron que la magnitud del ángulo de inclinación influye fuertemente la evolución de la pluma en el acuífero anisotrópico y heterogéneo estudiado. La velocidad poral promedio retardada del agua de poros (v/R) del modelo de adsorción controla significativamente la propagación horizontal de la pluma. La pluma de fondo está intensivamente retardada en las zonas de los lentes inclinados de más baja conductividad hidráulica y en las condiciones del fondo de no flujo. Las implicancias de estos hallazgos son muy importantes para el manejo de los acuíferos heterogéneos contaminados.

摘要

通过具倾斜各相异性的非均质含水层稳定流和溶质运移模拟可以了解倾角和吸附非均质性对非均质介质中溶质运移机制的影响. 诸多活性和非活性污染物在各种非均质含水层中的运移均能用模拟手段来研究. 非均质含水层的渗透系数 (K) 可用基于高斯相关频谱的HYDRO_GEN软件求出. 而吸附分布系数 (K _d), 则通过球面颗粒模型, 得出lnK 和 lnK _d 间存在显著的负相关关系. 求得的K和K _d导入地下水水流模型和溶质运移模型, 用于调查倾斜沉积各相异性对污染晕变化的影响. 模拟结果显示, 沉积倾角幅度在很大程度上控制着各向异性和非均质含水层中的污染晕变化. 吸附模型中缓慢的平均孔隙水流速 (v/R) 明显控制污染晕在水平方向上的扩散. 倾斜的低渗透系数透镜体和无流量底部之间地带, 污染晕底部强烈延迟. 上述发现对污染的非均质含水层管理具有重要的指示作用.

Resumo

A influência combinada de camadas inclinadas e de heterogeneidade da adsorção nos mecanismos de transporte de solutos em meios heterogéneos pode ser entendida através de simulações de fluxo estacionário e de transporte transitório num aquífero heterogéneo com anisotropia inclinada. Estudam-se, por simulações, o transporte de contaminantes reativos e não reativos em vários tipos de aquíferos heterogéneos. A condutividade hidráulica (K) dos aquíferos heterogéneos é gerada pelo HYDRO_GEN, com um espetro de correlação gaussiana. Considerando a heterogeneidade do coeficiente de distribuição da adsorção (K _d ), é obtida uma correlação negativa perfeita entre lnK e lnK _d usando o modelo de grãos esféricos. Os K e K _d gerados são usados como entrada para os modelos de fluxo de água subterrânea e de transporte e para investigar os efeitos da heterogeneidade sedimentar inclinada na evolução da pluma de contaminação. Os resultados da simulação mostraram que a magnitude do ângulo de inclinação influencia fortemente a evolução da pluma no aquífero heterogéneo e anisotrópico estudado. A velocidade média retardada da água nos poros (v/R) no modelo de adsorção controla significativamente a expansão horizontal da pluma. A pluma da base é intensamente retardada nas zonas situadas entre as lentes inclinadas de mais baixa condutividade hidráulica e as fronteiras de não-fluxo da base. As implicações destas conclusões são muito importantes para a gestão dos aquíferos heterogéneos contaminados.

Appendix: Derivation of equivalent hydraulic conductivity for heterogeneous aquifers

The equivalent hydraulic conductivity of a thick heterogeneous aquifer which consists of a series of thin parallel homogeneous layers was given by Bear (1972). By assuming the groundwater flow direction is parallel and perpendicular to the homogenous layer (see Figs.  5.8.1 and 5.8.2 of Bear 1972), the equivalent hydraulic conductivities are given by Eqs. (3) and (4), respectively

$$ {\overline{K}}^P={\displaystyle \sum_{\mathrm{i}=1}^N{K}_{\mathrm{i}}{b}_{\mathrm{i}}}/{\displaystyle \sum_{\mathrm{i}=1}^N{b}_{\mathrm{i}}} $$

(3)

$$ b/{\overline{K}}^N={\displaystyle \sum_{\mathrm{i}=1}^N\left({b}_{\mathrm{i}}/{K}_{\mathrm{i}}\right)} $$

(4)

where ${\overline{K}}^P$ and ${\overline{K}}^N$ [L/T] are the equivalent hydraulic conductivities for the flow parallel and perpendicular to the homogenous layers, respectively; K _i [L/T] and b _i [L] are the hydraulic conductivity and thickness of the thin homogenous layer, respectively; and N is the number of the thin layers.

Assuming N is equal to 2, it is easily demonstrated that ${\overline{K}}^P>{\overline{K}}^N$; in other words, the scenario of equivalent hydraulic conductivity of parallel flow is larger than that of perpendicular flow, which was demonstrated by Bear (1972). It is well known that refraction occurs at the interface of different layers under the flow oblique to the layer. The relationship between the hydraulic conductivity (K) and the refraction angle (δ) is given by

$$ \frac{K_{\mathrm{h}}}{K_{\mathrm{l}}}=\frac{ \tan {\delta}_{\mathrm{l}}}{ \tan {\delta}_{\mathrm{h}}} $$

(5)

where K _h and K _l represent the high and low hydraulic conductivity layers; δ _h and δ _l are the refraction angle of the high and low hydraulic conductivity layers, respectively.

In order to derive an equivalent hydraulic conductivity for the flow passing through a heterogeneous aquifer with variable dip angles (see Fig.  5.8.4 of Bear 1972), Eq. (5) was substituted into Eqs. (3) and (4) by Bear (1972), which leads to

$$ \frac{1}{{\overline{K}}^{\delta }}=\frac{{ \sin}^2{\delta}_{\mathrm{e}}}{{\overline{K}}^N}+\frac{{ \cos}^2{\delta}_{\mathrm{e}}}{{\overline{K}}^P} $$

(6)

where ${\overline{K}}^{\delta }$ [L/T] is the equivalent hydraulic conductivity of the dipping homogeneous aquifer; δ is the dip angle of the homogeneous aquifer; and δ _e is the acute angle between the flow direction and the interface of the homogeneous aquifers. The detailed derivation of Eqs. (3), (4) and (6) mentioned in the preceding was given by Bear (1972) and references therein.