Analysis of radial movement of an unconfined leaky aquifer due to well pumping and injection

Radial movement of an unconfined leaky aquifer was studied with respect to hydraulic forces that are induced by well recharge and discharge. New analytic solutions in the velocity and displacement fields were found and applied to describe transient movement in an unconfined leaky aquifer. Linear momentum and mass balance of saturated porous sediments, the Darcy-Gersevanov law, and the analytic solution of hydraulic drawdown for unsteady flow within the unconfined leaky aquifer were introduced to find the new solutions. Analytic results indicate that the nonlinear relation between the initial hydraulic head (h₀) and the well function has an insignificant effect on the aquifer transient movement when the drawdown s<0.02h ₀. When the well function is simplified with different assumptions and pumping conditions, the new solutions correspondingly reduce to cases that are similar to the Hantush-Jacob, Muskat, and Theis transient movement of a confined leaky aquifer. It was found that large leakance is important in slowing radial movement and reducing aquifer deformation. Flow velocity in the aquifer is more responsive to leakance than to cumulative displacement within the aquifer. The zones and boundary with tensile stress can be located using the same approach applied to a confined aquifer for risk assessment of earth fissuring.

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Résumé Le mouvement radial dans un aquifère semi-perméable libre a été étudié en considérant les forces hydrauliques induites par la recharge et le prélèvement au niveau d’un puits. De nouvelles solutions analytiques des champs de vitesse et de déplacement ont été trouvées et appliquées pour décrire le mouvement transitoire dans un aquifère semi-perméable libre. Pour trouver les nouvelles solutions, le moment linéaire et le bilan de masse dans les sédiments poreux saturés, la loi de Darcy-Gersevanov, et la solution analytique du rabattement hydraulique pour un écoulement transitoire dans un aquifère semi-perméable libre sont pris en compte. Les résultats analytiques montrent que la relation non-linéaire entre le potentiel hydraulique initial (h₀) et la fonction de puits a un effet insignifiant sur le mouvement transitoire de l’aquifère quand le rabattements s <0.02h₀. Si la fonction de puits est simplifiée en tenant compte de différentes hypothèses et conditions de pompage, les nouvelles solutions se réduisent en conséquence à des cas similaires au mouvement transitoire dans un aquifère semi-perméable captif selon Hantush-Jacob, Muskat, et Theis. Il s’est avéré qu’une drainance élevée est importante pour le ralentissement du mouvement radial et la réduction de la déformation de l’aquifère. La vitesse d’écoulement dans l’aquifère est plus sensible à la drainance qu’au déplacement cumulé dans l’aquifère. Les zones et la frontière présentant des contraintes de traction peuvent être localisées en utilisant la même approche appliquée à un aquifère captif pour l’évaluation des risques de fissuration du sol.

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Resumen Se ha estudiado el movimiento radial en un acuífero no confinado con fuga en relación a las fuerzas hidráulicas que son inducidas por la descarga y recarga del pozo. Se encontraron nuevas soluciones analíticas en los campos de desplazamiento y velocidad, las cuales se aplicaron para describir el movimiento transitorio en un acuífero no confinado con fuga. Se han introducido cálculos de balance de masa y momentum lineal de los sedimentos porosos saturados, la Ley Darcy-Gersevanov, y la solución analítica de descenso hidráulico para flujo sin régimen permanente dentro del acuífero no confinado con goteo para encontrar las nuevas soluciones. Los resultados analíticos indican que la relación no lineal entre la presión hidráulica inicial (h₀) y la función del pozo tiene efecto insignificante en el movimiento transitorio del acuífero cuando el descenso s < 0.02h₀. Cuando se simplifica la función del pozo en base a diferentes supuestos y condiciones de bombeo se reducen las nuevas soluciones a casos que son similares a el movimiento transitorio Hantush-Jacob, Muskat, y Theis de un acuífero confinado con goteo. Se encontró que las fugas grandes son importantes en la disminución del movimiento radial y en la reducción de la deformación del acuífero. La velocidad de flujo en el acuífero responde más a las fugas que al desplazamiento acumulativo dentro del acuífero. Pueden localizarse zonas y límites con esfuerzos tensionales usando el mismo enfoque aplicado a acuíferos confinados para evaluación de riesgo de generación de fracturas en el terreno.

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Approximate analytical and numerical solutions for radial non‐Darcian flow to a well in a leaky aquifer with wellbore storage and skin effect

This study investigated non‐Darcian flow to a well in a leaky aquifer considering wellbore storage and a finite‐thickness skin. The non‐Darcian flow is described by the Izbash equation. We have used a linearization procedure associated with the Laplace transform to solve such a non‐Darcian flow model. Besides, the Stehfest method has been used to invert the Laplace domain solutions for the drawdowns. We further analyzed the drawdowns inside the well for different cases. The results indicated that a smaller B_D results in a smaller drawdown at late times and the leakage has little effect on the drawdown inside the well at early times, where B_D is a dimensionless parameter reflecting the leakage. We have also found that the flow for the negative skin case approaches the steady‐state earlier than that for the positive skin. In addition, the drawdown inside the well with a positive skin is larger than that without skin effect at late times, and a larger thickness of the skin results in a greater drawdown inside the well at late times for the positive skin case. A reverse result has been found for the negative skin case. Finally, we have developed a finite‐difference solution for such a non‐Darcian flow model and compared the numerical solution with the approximate analytical solution. It has been shown that the linearization procedure works very well for such a non‐Darcian flow model at late times, and it underestimates the drawdowns at early times. Copyright © 2012 John Wiley & Sons, Ltd.     

用水位恢复数据反演越流承压含水层参数

水文地质勘测中,由于水位恢复阶段没有人力和机械因素干扰,由测量数据可以画出平滑的曲线,更适宜于分析水文地质参数,但经典非稳定流Theis公式和Theis水位恢复法所依据的若干假设条件在实际中难以满足。针对越流承压含水层具有补给条件而很快稳定以及非稳定抽水阶段流量常“抖动”的特点,论证了利用稳定流量和Hantush-Jacob越流模型计算的可行性,并用扩展的卡尔曼滤波器反演水文地质参数,经文献中历史数据和实地抽水试验检验结果表明,由该方法反演的预测值和实测值吻合良好。     

承压含水层井流-盖层弯曲效应的解析理论

指出承压含水层盖层的弯曲变形与开采井周围的径向地下水运动存在相互作用, 而这一效应在传统的井流理论中没有被认识到.通过引入弹性薄板理论, 建立了无越流的承压含水层井流-顶板弯曲效应的解析模型, 同时考虑了含水层和水的压缩性, 结果表明Theis井流方程给出的抽水降深偏小.在此基础上推导了有越流承压含水层井流-盖层弯曲效应的偏微分方程, 求出了解析解, 并与传统理论的结果进行了对比, 表明Hantush-Jacob公式计算的降深也是偏小的.在抽水井附近和抽水初期, 传统理论可能导致显著的相对误差.      

越流含水层井群系统地下水流的边界元数值模拟

本文提出一种求解越流含水层井群系统的边界元方法。该法把抽水井井壁作为内边界,通过积分处理,不需要对井壁内边界进行剖分,通过推导求得水头H及其法向导数的边界积分方程,离散化后得到求解该积分方程的一组线性代数方程组、该法用于实例计算表明,计算精度较高。     

求取道路结构型地层瑞利波频散曲线的方法

求取道路结构型地层的瑞利波频散曲线,过去一般是采用刚度矩阵法、有限单元法等方法在复数域进行求解.作者在吸取前人某些研究思路的基础上,提出了添加附加层的方法,使原复数域的求解问题转化到实数域进行,然后用二分法进行求解.附加层法提高了正演计算的速度,且模拟计算结果表明了新方法的可行性.     

A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

常规越流承压含水层影响半径计算方法之改进

影响半径是一个有争议的概念,针对不同含水层和计算模型各有不同的计算方式,而在工程应用中常使用理论依据不甚明确的经验公式。针对可形成稳定流的越流承压含水层,展开对确定其影响半径的常用方法即3个及以上观测孔稳定流阶段降深-距离直线图解法的分析,认为这一方法容易造成工程师对影响半径的误判,指出其易于误读之处并对使用该法提出了修正建议。     

Tide‐induced groundwater head fluctuation in a coastal aquifer system with a submarine outcrop covered by a thin silt layer

We present an analytical solution of groundwater head response to tidal fluctuation in a coastal multilayered aquifer system consisting of an unconfined aquifer, a leaky confined aquifer and a semi‐permeable layer between them. The submarine outcrop of the confined aquifer is covered by a thin silt layer. A mathematical model and the analytical solution of this model are given. The silt layer reduces the amplitude of the hydraulic head fluctuation by a constant factor, and shifts the phase by a positive constant (time lag), both of which depend on the leakances of the silt layer and the semi‐permeable layer. The time lag is less than 1·5 h and 3·0 h for semi‐diurnal and diurnal sea tides respectively. When the leakance of the semi‐permeable layer or the silt layer assumes certain special values, the solution becomes the existing solutions derived by previous researchers. The amplitude of the hydraulic head fluctuation in the confined aquifer increases with the leakance of the silt layer and decreases with the leakance of the semi‐permeable layer, whereas the phase shift of the fluctuation decreases with both of them. A hypothetical example shows that neglecting the silt layer may result in significant parameter estimation discrepancy between the amplitude attenuation and the time‐lag fittings. Copyright © 2007 John Wiley & Sons, Ltd.