Abstract
The distribution of saline water in the upper aquifer and freshwater in the lower aquifer is a characteristic of groundwater resources in the North China Plain (NCP). The phenomenon of groundwater depression cones in confined aquifers, primarily caused by excessive groundwater extraction, has been extensively documented. In line with Darcy’s law, it is noteworthy that the migration of shallow groundwater into confined aquifers can occur due to a substantial difference in hydraulic head between the unconfined and confined aquifer systems. However, based on the monitoring data, the quality of deep groundwater generally remains good. This paper attempts to explain this phenomenon from the perspective of non-Darcian flow in aquitards. A finite difference method is used to solve low-velocity non-Darcian flow to a well in the NCP. The mathematical model considers the threshold pressure gradient to describe non-Darcian flow in the aquitard and assumes Darcian and horizontal flows for both shallow and confined aquifers. The comparison with traditional Darcian flow indicates that the leaky area decreases rapidly when considering the threshold pressure gradient. The leaky area is negatively correlated with the aquitard thickness and the transmissivity of the confined aquifer, and positively correlated with the pumping rate. The non-Darcian vertical flow velocity is significantly lower than that obtained from Darcian theory. The vertical velocity difference between Darcian and non-Darcian flows is significant under the situation of a small aquitard thickness, large pumping rate, low transmissivity and large leakage coefficient when the threshold pressure gradient is large.
Résumé
La répartition eau salée dans l’aquifère supérieur et eau douce dans l’aquifère inférieur est une caractéristique des ressources en eau souterraine de la Plaine du Nord de la Chine. Le phénomène des cônes de dépression dans les aquifères captifs, principalement causé par une exploitation excessive des eaux souterraines, a été largement documenté. En cohérence avec la loi de Darcy, il faut noter que la migration des eaux souterraines peu profondes au sein des aquifères captifs peut se produire à la suite d’une différence substantielle des charges hydrauliques entre les systèmes aquifères captifs et non captifs. Cependant, d’après les données de surveillance, la qualité des eaux souterraines profondes reste généralement bonne. Le présent article tente d’expliquer ce phénomène dans le contexte d’un écoulement non-Darcien dans des aquifères semi-captifs. La méthode des différences finies est utilisée pour résoudre un écoulement lent non-Darcien vers un puits situé dans la Plaine du Nord de la Chine. Le modèle mathématique prend en compte un gradient de pression seuil pour décrire l’écoulement non-Darcien dans l’aquifère semi-captif et suppose des écoulements Darciens horizontaux à la fois dans les aquifères peu profonds et les aquifères captifs. La comparaison avec un écoulement Darcien classique montre que la zone de fuite décroît rapidement quand on considère le gradient de pression seuil. La superficie de la zone de fuite est corrélée négativement à l’épaisseur de l’aquifère semi-captif et la transmissivité de l’aquifère captif est corrélée positivement au débit de pompage. La vitesse de l’écoulement vertical non-Darcien est significativement plus faible que celle obtenue à partir de la théorie de Darcy. La différence de vitesse verticale entre les écoulements Darciens et non-Darciens est importante dans le cas d’une épaisseur faible de l’aquifère semi-captif, d’un débit de pompage élevé, d’une transmissivité faible et d’un coefficient de fuite important si le gradient de pression seuil est élevé.
Resumen
Una característica de los recursos hídricos subterráneos de la Llanura del Norte de China (NCP) es la distribución de agua salina en el acuífero superior y de agua dulce en el acuífero inferior. El fenómeno de los conos de depresión de aguas subterráneas en acuíferos confinados, causado principalmente por la extracción excesiva de agua subterránea, ha sido ampliamente documentado. De acuerdo con la ley de Darcy, cabe señalar que la migración de aguas subterráneas poco profundas hacia acuíferos confinados puede producirse debido a una diferencia sustancial de altura hidráulica entre los sistemas acuíferos no confinados y confinados. Sin embargo, según los datos de seguimiento, la calidad de las aguas subterráneas profundas suele seguir siendo buena. En este artículo se intenta explicar este fenómeno desde la perspectiva del flujo no darciano en acuíferos. Se utiliza un método de diferencias finitas para resolver el flujo no darciano de baja velocidad hacia un pozo en el NCP. El modelo matemático considera el gradiente de presión del umbral para describir el flujo no darciano en el acuitardo y asume flujos darcianos y horizontales tanto para acuíferos someros como confinados. La comparación con el flujo darciano tradicional indica que el área de filtración disminuye rápidamente al considerar el gradiente de presión del umbral. El área de filtración está negativamente correlacionada con el espesor del acuitardo y la transmisividad del acuífero confinado, y positivamente correlacionada con la tasa de bombeo. La velocidad de flujo vertical no darciana es significativamente inferior a la obtenida a partir de la teoría darciana. La diferencia de velocidad vertical entre los flujos darcianos y no darcianos es significativa en una situación de pequeño espesor del acuitardo, elevado caudal de bombeo, baja transmisividad y alto coeficiente de filtración cuando el gradiente de presión del umbral es elevado.
摘要
上层含水层盐水和下层含水层淡水的分布是华北平原(NCP)地下水资源的特征。由于过度抽取地下水引起承压含水层中地下水降落漏斗的出现。根据达西定律, 在潜水和承压水巨大的水头差作用下, 潜水将越流补给承压水。然而, 根据监测数据, 深层地下水的水质依然保持良好。本文试图从弱透水层非达西流动的角度解释这一现象, 使用有限差分法求解NCP的低速非达西流的井流问题。该数学模型考虑了启动压力梯度以描述弱透水层中的非达西流动, 并假设潜水含水层和承压含水层中的水流均为达西水平流动。与传统的达西流相比, 考虑了启动压力梯度时, 越流区迅速减小。越流区与弱透水层厚度和承压含水层导水系数呈负相关, 与抽水率呈正相关。非达西垂向流动速度明显低于达西理论得到的垂向速度。在启动压力梯度较大的情况下, 当弱透水层厚度较小、抽水率较大、导水系数较低、越流系数较大时, 达西流动与非达西流动之间的垂向速度差异显著。
Resumo
A distribuição de água salina no aquífero superior e de água doce no aquífero inferior é uma característica dos recursos hídricos subterrâneos na Planície Norte da China (PNC). O fenômeno dos cones de depressão das águas subterrâneas em aquíferos confinados, causado principalmente pela extração excessiva de águas subterrâneas, tem sido extensivamente documentado. De acordo com a lei de Darcy, é digno de nota que a migração de águas subterrâneas rasas para aquíferos confinados pode ocorrer devido a uma diferença substancial na carga hidráulica entre os sistemas aquíferos livres e confinados. Contudo, com base nos dados de monitoramento, a qualidade das águas subterrâneas profundas permanece geralmente boa. Este artigo tenta explicar este fenômeno a partir da perspectiva do fluxo não-Darciano em aquitardos. Um método de diferenças finitas é usado para resolver o fluxo não-Darciano de baixa velocidade para um poço na PNC. O modelo matemático considera o gradiente de pressão limiar para descrever o fluxo não-Darciano no aquitardo e assume fluxos Darcianos e horizontais para aquíferos rasos e confinados. A comparação com o fluxo Darciano tradicional indica que a área de drenança diminui rapidamente quando se considera o gradiente de pressão limite. A área drenada está negativamente correlacionada com a espessura do aquitardo e a transmissividade do aquífero confinado, e positivamente correlacionada com a taxa de bombeamento. A velocidade do fluxo vertical não-Darciano é significativamente menor do que a obtida pela teoria Darciana. A diferença de velocidade vertical entre fluxos Darcianos e não-Darcianos é significativa na situação de pequena espessura de aquitardo, grande taxa de bombeamento, baixa transmissividade e grande coeficiente de drenagem quando o gradiente de pressão limite é grande.
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This research was supported by National Natural Science Foundation of China (51979252, 52279025) and China Scholarship Council (CSC) (202106415007).
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Meng, X., Yan, G., Shen, L. et al. How low-velocity non-Darcian flow in low-permeability media controls the leakage characteristics of a leaky aquifer system. Hydrogeol J 32, 541–555 (2024). https://doi.org/10.1007/s10040-023-02764-w
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DOI: https://doi.org/10.1007/s10040-023-02764-w