Abstract
Groundwater can be contaminated by natural or manmade activities. The quality of groundwater is affected by increased levels of contaminants in effluents from industries, pesticides from agriculture, septic systems, landfills, leakage from fuel tanks, toxic chemical spills, etc. There are various methods available for numerical modeling of contaminant transport, which include the finite difference method, finite element method, boundary element method, etc. Meshless methods are a new class of techniques that are gaining popularity because they have certain benefits over conventional approaches. Based on the formulation approach, meshless methods may be divided into two types: strong and weak. In this study, the local radial point interpolation method (LRPIM), a meshless weak form formulation, is developed to simulate the flow and contaminant movement in groundwater. LRPIM uses the multiquadric radial basis function (MQ-RBF) for shape function evaluation. Here, a LRPIM-based coupled flow and transport (CFT) model is developed. The model is applied to verify test problems and a field case study. For the test problem, the results obtained are checked against the available analytical solutions and found to give good accuracy. The model is then applied to a real aquifer with chloride contamination from industry. Two different cases, of (1) initial concentration with continuous release of contaminant, and (2) initial concentration with no further release of contaminant, were considered. The LRPIM model predictions are satisfactory and comparable to the results of standard MODFLOW/MT3DMS models. As shown in the study, the LRPIM–CFT model can be effectively used for large-scale field-level aquifer problems.
Résumé
Les eaux souterraines peuvent être contaminées par des causes naturelles ou des activités humaines. La qualité des eaux souterraines est affectée par des niveaux croissants de contaminants dans les effluents industriels, les pesticides provenant de l’agriculture, les systèmes septiques, les décharges, les fuites sur des stockages de fuel, les déversements de produits chimiques toxiques, etc. Il existe diverses méthode numériques disponibles pour modéliser le transport de contaminant, elles comprennent: la méhode par différences finies, la méthode par éléments finis, la méthode par limites finies, etc. Les méthodes sans maillage forment une classe nouvelle de techniques qui gagnent en popularité parce qu’elles présentent certains avantages sur les approches conventionnelles. Sur la base de l’approche de formulation, les méthodes sans maillage peuvent être réparties en deux types: fort et faible. Dans la présente étude, la méthode d’interpolation par point radial local (MIPRL), une formulation de forme faible sans maillage, est développée pour simuler l’écoulement et le déplacement du contaminant dans les eaux souterraines. MIPRL utilise la fonction de base radiale multiquadratique (MQ-FBR) pour évaluer la fonction de forme. Ici, un MIPRL basé sur un modèle couplé écoulement et transport (CET) est développé. Le modèle est appliqué pour vérifier les problèmes de test et une étude de cas sur le terrain. Pour le problème du test, les résultats obtenus sont vérifiés au regard des solutions analytiques disponibles et on estime qu’ils sont d’une bonne précision. Le modèle est ensuite appliqué à un aquifère réel avec une contamination par des chlorures industriels. Deux cas différents (1) une concentration initiale avec un largage continu de contaminant, et (2) une concentration initiale sans relargage de contaminant ensuite, ont été considérés. Les prédictions du modèle MIPRLsont satisfaisantes et comparables aux résultats des modèles standards MODFLOW/MT3DMS. Comme le montre l’étude, le modèle MIPRL-CET peut être efficacement utilisé pour les problèmes d’un aquifère à grande échelle au niveau du terrain.
Resumen
Las aguas subterráneas pueden estar contaminadas por actividades naturales o artificiales. La calidad del agua subterránea se ve afectada por el aumento de los contaminantes en los efluentes de las industrias, los pesticidas de la agricultura, los sistemas sépticos, los vertederos, las fugas de los depósitos de combustible, los vertidos de productos químicos tóxicos, etc. Hay varios métodos numéricos disponibles para la modelización del transporte de contaminantes, que incluyen el método de las diferencias finitas, el método de los elementos finitos, el método de los elementos límite, etc. Los métodos sin malla son una nueva clase de técnicas que están adquiriendo notoriedad porque presentan ciertas ventajas con respecto a los enfoques convencionales. Basándose en el enfoque de la formulación, los métodos sin malla pueden dividirse en dos tipos: fuertes y débiles. En este estudio, se desarrolla el método de interpolación local de puntos radiales (LRPIM), una formulación débil sin malla, para simular el flujo y el movimiento de contaminantes en aguas subterráneas. LRPIM utiliza la función de base radial multicuádrica (MQ-RBF) para la evaluación de la función de forma. Aquí se desarrolla un modelo de flujo y transporte acoplado (CFT) basado en LRPIM. El modelo se aplica para verificar problemas de prueba y un caso de estudio de campo. En el caso del problema de prueba, los resultados obtenidos se comparan con las soluciones analíticas disponibles y se comprueba que ofrecen una buena precisión. A continuación, el modelo se aplica a un acuífero real con contaminación por cloruros procedente de la industria. Se consideraron dos casos diferentes, de (1) concentración inicial con liberación continua de contaminante, y (2) concentración inicial sin liberación adicional de contaminante. Las predicciones del modelo LRPIM son satisfactorias y comparables a los resultados de los modelos estándar MODFLOW/MT3DMS. Como se muestra en el estudio, el modelo LRPIM-CFT puede ser utilizado eficazmente para problemas de acuíferos a gran escala a nivel de campo.
摘要
地下水可能受到自然或人为活动的污染。地下水质量受到工业废水排放、农业杀虫剂、化粪池系统、垃圾填埋场、燃料箱泄漏、有毒化学品泄漏等污染物级别增加的影响。有多种数值方法可用于污染物迁移建模,包括有限差分法、有限元法、边界元法等。无网格法是一类新的技术, 由于与传统方法相比具有一定的优势, 因此越来越受欢迎。基于公式化方法, 无网格方法可分为**和弱两种类型。在本研究中, 开发了无网格的弱形式公式的局部径向点插值法(LRPIM),用于模拟地下水中的水流和污染物运动。LRPIM 使用多重二次径向基函数(MQ-RBF) 进行形状函数评估。开发了基于 LRPIM 的耦合水流和传输(CFT)模型。该模型用于验证测试案例和现场案例研究。对于测试案例, 根据可用的解析解核对计算的结果, 并发现其具有良好的准确性。然后将该模型应用于工业氯化物污染的真实含水层。考虑了两种不同的情况,(1) 持续释放污染物的初始浓度, 和 (2) 没有进一步释放污染物的初始浓度。 LRPIM 模型的预测结果令人满意,与标准 MODFLOW/MT3DMS 模型的结果相当。研究表明, LRPIM-CFT 模型可以有效地用于解决大规模场地级含水层问题。
Resumo
Águas subterrâneas podem ser contaminadas por atividades naturais ou antrópicas. A qualidade das águas subterrâneas é afetada pelo crescimento de níveis de contaminantes em efluentes das indústrias, pesticidas da agricultura, sistemas sépticos, aterros, vazamentos de tanques de combustíveis, derramamento de químicos tóxicos etc. Existem vários métodos numéricos disponíveis na modelagem de transporte de contaminante, que incluem o método da diferença finita, método do elemento finito, método do elemento limite etc. Métodos sem malha são uma nova classe de técnicas que estão ganhando popularidade por possuírem certos benefícios sobre abordagens convencionais. Baseado na abordagem de formulação, métodos sem malha podem ser divididos em dois tipos: forte e fraco. Nesse estudo, o método de interpolação de ponto radial local (MIPRL), uma formulação fraca sem malha, é desenvolvido para simular o fluxo e movimento do contaminante nas águas subterrâneas. MIPRL utilizam uma função radial de base multiquadrática (FRBMQ) para avaliação da função da forma. Aqui, um modelo baseado no MIPRL de fluxo e transporte acoplado (FTA) foi desenvolvido. O modelo foi aplicado para verificar problemas-teste e estudo de caso de campo. Para o problema-teste, os resultados obtidos são checados contra as soluções analíticas disponíveis e encontram para dar uma boa acurácia. O modelo é então aplicado para um aquífero real com contaminação de cloreto por uma indústria. Dois casos diferentes, de (1) concentração inicial com liberação contínua de contaminante, e (2) concentração inicial sem liberação de contaminante, foram considerados. As previsões do modelo MIPRL são satisfatórias e comparáveis aos resultados dos modelos-padrão MODFLOW/MT3DMS. Como mostrado no estudo, o modelo MIPRL-FTA pode ser efetivamente utilizado para problemas de aquífero a nível de campo de larga escala.
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The authors are thankful to the Bhabha Atomic Research Centre, Mumbai, and the Indian Institute of Technology Bombay for providing the facilities to carry out the work.
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Swetha, K., Eldho, T.I., Singh, L.G. et al. Simulation of coupled flow and contaminant transport in an unconfined aquifer using the local radial point interpolation meshless method. Hydrogeol J 31, 485–500 (2023). https://doi.org/10.1007/s10040-022-02558-6
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DOI: https://doi.org/10.1007/s10040-022-02558-6