Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge Condition

Abstract

This paper presents closed form solution for unsteady flow equation corresponding to the transient hydraulic head, flow rate and volumetric exchange of a confined aquifer which is in contact with a constant piezometric head at one end and a stream whose water level is rising at a constant rate at the other end. The aquifer is also subjected to receive constant inflow due to rain infiltration. The unsteady groundwater flow equation is solved using Laplace transform to get analytical expressions for the transient hydraulic head and flow rate at the left and right interfaces and the net volumetric exchange of water at the aquifer-stream interface. The analytical results presented here show the effect of recharge due to rain infiltration on the net volumetric exchange and reveal the conditions for which net inflow in the aquifer could be positive, negative or zero. The results obtained have the capability to determine transient hydraulic head for two extreme scenarios: (i) very slow rise and (ii) very fast rise in the stream water. Analytical result show that the net volumetric exchange could be positive, zero or negative depending on the surface infiltration and stream water rise rate. Príspevok obsahuje analytické riešenie rovnice neustáleného prúdenia vzhľadom na neustálenú hydraulickú výšku, rýchlosť prúdenia a objemové toky vo zvodnenom kolektore s napätou hladinou, ktorý je v kontakte s konštantnou piezometrickou výškou na jednej strane a s tokom s konštantne sa zvyšujúcou hladinou vody na strane druhej.Zvodnený kolektor je tiež napájaný konštantnou rýchlosťou infiltrovanou vodou zo zrážok. Rovnica neustáleného prúdenia podzemnej vody je riešená s použitím Laplaceovej transformácie, aby sme získali neustálenú tlakovú výšku na ľavej aj pravej strane a objemový prítok vody na rozhraní zvodnený kolektortok.Výsledky analytického riešenia, ktoré predkladáme, ukazujú vplyv infiltrácie zrážok na doplňovanie podzemnej vody a odhaľujú podmienky, za ktorých prítok do zvodneného kolektora môže byť kladný, negatívny, alebo nulový. Získané výsledky umožňujú určiť neustálené hydraulické výšky pre dva extrémne scenáre: (i) veľmi pomalé a (ii) veľmi rýchle zvýšenie hladiny vody v toku. Analytické riešenie ukazuje, že objem vody, ktorou je zvodnený kolektor doplňovaný, môže byť kladný, záporný, alebo nulový, v závislosti na intenzite infiltrácie a rýchlosti zvyšovania sa hladiny vody v toku.KĽÚČOVÉ SLOVÁ: piezometrická výška, rýchlosť prúdenia, prítok do podzemných vôd, ohraničený zvodnený kolektor, analytické riešenia, Laplaceova transformácia.

Modeling the river-aquifer via a new exact model under a more general function of river water level variation

“…The accuracy and ability of the present new exact model, in the special case of linear river water variation, is verified by the results obtained from the analytical solution of Bansal and Das (2009). For the special case of (u 2 = 0, u 1 = 1 day −1 and m = 1), Eq.…”

“…They investigated a simplified situation where a homogeneous confined layer is in contact with a stream whose level is rising linearly at a constant speed. Bansal and Das (2009) extended this model to an aquifer under recharge condition. The aforementioned solutions are obtained for a confined horizontal aquifer.…”

“…A leaky, isotropic, incompressible and homogeneous aquifer, which is in contact with a constant river level at one end and a river of varying water level at the other end, has been investigated. A hypothetical example is considered to compare the results of the presented new exact models with the results of the exact model of Bansal and Das (2009) as well as MODFLOW. The results show that the presented new exact models are accurate, robust and efficient.…”

New analytical solution for stream–aquifer interaction under constant replenishment

“…Xie and Yuan (2010) developed a statistical-dynamical scheme for water table prediction under stream-aquifer interaction in an arid region. Bansal and Das (2009) and Bansal (2014) obtained new analytical solutions of a linearized Boussinesq equation characterizing groundwater flow in a stream-unconfined aquifer. In the present paper, approximate analytical solution for interaction between stream and unconfined aquifer is obtained assuming one-dimensional horizontal groundwater flow in homogeneous and isotropic aquifer.…”

Numerical Analysis of Drawdown in an Unconfined Aquifer due to Pumping Well by SIGMA/W and SEEP/W Simulations

“…Aquifers provide water to wells from there it can be pumped out. Open wells, bore wells and tubewells are manmade mechanisms used to extract a groundwater [3]. Aquifers also fed streams and rivers, especially during the dry season.…”