Abstract
Fracture conduits serve as the primary channels for groundwater runoff in karst areas, controlling the water level and distribution of flow in the groundwater system. To determine the parameters of fracture-conduit karst systems and to analyze the distribution characteristics of the pressure field and flow field, a pipe network calculation method is presented that discretizes the fracture medium and conduit medium into pipes and nodes. The connection rules for nodes and pipes are established, and different water conductivity coefficients are assigned to discrete pipes. Based on the principles of conservation of mass and energy, nonhomogeneous linear control equations are constructed to represent the discrete pipe network (PN). By solving the equations, groundwater parameters can be calculated for the PN. Meanwhile, a laboratory model test was conducted to validate the PN, and the numerical calculation results aligned well with the laboratory test results. In addition, a simple case is compared and verified, and the calculation results are compared with those obtained using the multiphysics software, COMSOL. The results indicate that the PN method can achieve more accurate calculation results with fewer elements. The method calculates the distribution characteristics of the flow field within the water-conducting medium and elucidates the influence of the properties of the medium on the distribution characteristics of the flow field. The research results provide guidance for the distribution of groundwater flow fields in karst areas and are expected to be applied to calculating groundwater pressures and flows in large-scale fracture-conduit systems.
Résumé
Les conduits de fracture servent de canaux principaux pour le ruissellement des eaux souterraines dans les zones karstiques, contrôlant le niveau d’eau et la répartition du flux dans le système d’eau souterraine. Pour déterminer les paramètres des systèmes karstiques de type fracture-conduit et pour analyser les caractéristiques de distribution du champ de pression et du champ d’écoulement, une méthode de calcul de réseau de tuyaux est présentée discrétisant le milieu de fractures et le milieu de conduits en tuyaux et nœuds. Les règles de connexion des nœuds et des tuyaux sont établies et différents coefficients de conductivité hydraulique sont attribués aux tuyaux discrets. Basées sur les principes de conservation de la masse et de l’énergie, des équations de contrôle linéaires non homogènes sont construites pour représenter le réseau de tuyaux discrets (RT). En résolvant les équations, les paramètres des eaux souterraines peuvent être calculés pour le RT. Entre-temps, un test sur un modèle de laboratoire a été effectué pour valider le RT et les résultats des calculs numériques correspondent bien aux résultats des tests en laboratoire. De plus, un cas simple est comparé et vérifié, et les résultats des calculs sont comparés à ceux obtenus à l’aide du logiciel multiphysique COMSOL. Les résultats indiquent que la méthode RT peut obtenir des résultats de calcul plus précis avec moins d’éléments. Le procédé calcule les caractéristiques de distribution du champ d’écoulement dans le milieu conducteur d’eau et élucide l’influence des propriétés du milieu sur les caractéristiques de distribution du champ d’écoulement. Les résultats de la recherche fournissent des indications pour la répartition des champs d’écoulement des eaux souterraines dans les zones karstiques et devraient être appliqués au calcul des pressions et des flux des eaux souterraines dans les systèmes de fracture-conduits à grande échelle.
Resumen
Los conductos fracturados sirven de canales principales para la circulación de las aguas subterráneas en zonas kársticas, controlando el nivel del agua y la distribución del flujo en ese sistema. Para determinar los parámetros de los sistemas kársticos de conductos fracturados y analizar las características de distribución del campo de presión y de flujo, se presenta un método de cálculo de redes de tuberías que discretiza el medio de fractura y el medio de conductos en tuberías y nodos. Se definen las reglas de interconexión de estos nodos y tuberías, y se asignan distintos coeficientes de conductividad hidráulica a las tuberías discretas. Basándose en los principios de conservación de la masa y la energía, se construyen ecuaciones de control lineal no homogéneas para representar la red de tuberías discretas (PN). Resolviendo las ecuaciones, pueden calcularse los parámetros de las aguas subterráneas para la red de tuberías. Mientras tanto, se realizó una prueba de modelo de laboratorio para la validación y los resultados del cálculo numérico coinciden con los de la prueba de laboratorio. Además, se compara y verifica un caso simple, y los resultados del cálculo se comparan con los obtenidos utilizando el software multifísico, COMSOL. Los resultados indican que el método PN puede lograr resultados de cálculo más precisos con menos elementos. El método calcula las características de distribución del campo de flujo dentro del medio conductor de agua y dilucida la influencia de las propiedades del medio en las características de distribución del campo de flujo. Los resultados de la investigación proporcionan orientaciones para la distribución de los campos de flujo de aguas subterráneas en zonas kársticas y se espera que se apliquen al cálculo de las presiones y flujos de aguas subterráneas en sistemas de conducto-fractura a gran escala.
摘要
岩溶裂隙-管道作为主要的地下水径流通道, 控制着地下水系统的水位和流场分布。为了获取裂隙-管道型岩溶地下水参数与压强场、流场分布特征, 本文提出一种裂隙-管道型导水介质离散管网计算方法, 该方法将裂隙介质和管道介质离散为管道和节点组成的管网, 构建节点和管道的连接规则, 赋予离散管道不同的导水系数, 基于质量守恒和能量守恒, 最终构建求解离散管网方法的非齐次线性控制方程组。通过求解方程组, 实现管网地下水参数的计算。采用室内模型试验进行了管网方法的验证, 数值计算结果与室内试验结果吻合较好。此外, 进行了一个简单案例的验证, 并将计算结果与多物理场COMSOL软件的计算结果进行了对比,结果表明, 管网法能够利用较少的单元数量获得较准确的计算结果, 同时, 该方法准确地计算了导水介质中流场的分布特征, 揭示了导水介质的性质对流场的分布特性的影响。研究结果为岩溶地区地下水流场的分布提供了指导, 有望应用于大规模的管道裂隙介质地下水压力和流量的计算问题。
Resumo
Os conduítes de fratura servem como canais primários para o escoamento de águas subterrâneas em áreas cársticas, controlando o nível da água e a distribuição do fluxo no sistema de águas subterrâneas. Para determinar os parâmetros dos sistemas cársticos de fratura-conduíte e analisar as características de distribuição do campo de pressão e do campo de fluxo, é apresentado um método de cálculo de rede de tubos que discretiza o meio de fratura e o meio de conduíte em tubos e nós. As regras de conexão para nós e tubos são estabelecidas e diferentes coeficientes de condutividade da água são atribuídos a tubulações discretas. Com base nos princípios de conservação de massa e energia, equações de controle linear não homogêneas são construídas para representar a rede discreta de tubos (RDT). Ao resolver as equações, os parâmetros das águas subterrâneas podem ser calculados para a RDT. Entretanto, foi realizado um teste de modelo laboratorial para validar a RDT, e os resultados dos cálculos numéricos alinharam-se bem com os resultados dos testes laboratoriais. Além disso, um caso simples é comparado e verificado, e os resultados dos cálculos são comparados com aqueles obtidos utilizando o software multifísico COMSOL. Os resultados indicam que o método RDT pode alcançar resultados de cálculo mais precisos com menos elementos. O método calcula as características de distribuição do campo de fluxo dentro do meio condutor de água e elucida a influência das propriedades do meio nas características de distribuição do campo de fluxo. Os resultados da pesquisa fornecem orientação para a distribuição de campos de fluxo de águas subterrâneas em áreas cársticas e espera-se que sejam aplicados ao cálculo de pressões e fluxos de águas subterrâneas em sistemas de condutos de fratura em grande escala.
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The authors would like to thank the reviewers for their valuable suggestions and discussions, which helped to improve the manuscript.
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This research was supported by the Key Program of Shandong Provincial Natural Science Foundation of China [ZR2020KE006] and the Shandong Province Key R&D Program (Major Technological Innovation Project) [2021CXGCO10301, 2020CXGC011405].
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Yang, P., Li, T., Fan, Q. et al. Calculation of fracture-conduit karst groundwater pressures and flows using a pipe network method. Hydrogeol J (2024). https://doi.org/10.1007/s10040-024-02786-y
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DOI: https://doi.org/10.1007/s10040-024-02786-y