Steady groundwater flow in leaky multiple-aquifer systems

Hemker, C.J.

doi:10.1016/0022-1694(84)90089-1

Cited by 57 publications

(40 citation statements)

References 6 publications

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“…We have applied a generalized Fourier transform, specified by (12)(13)(14)(15)(16), and (21) to solve semi-analytically a longstanding problem in hydrology: three-dimensional transient flow in a coupled system of aquifers with z-dependence. This generalized Fourier transform, with the restriction d i = 0 in (13), has been applied succesfully in the past for cases where one has to deal only with just two independent variables (r and z (a stationary case); see [1].…”

Section: Discussionmentioning

confidence: 99%

“…This generalized Fourier transform, with the restriction d i = 0 in (13), has been applied succesfully in the past for cases where one has to deal only with just two independent variables (r and z (a stationary case); see [1]. It could be applied for the case with the independent variables t and z (an one-dimensional (vertical), transient case), and also in cases where one can justify the assumption that K h,i /S s,i = ρ is independent of i.…”

Section: Discussionmentioning

confidence: 99%

“…. is the mth eigenfunction of the generalized eigenvalue problem defined by (13)(14)(15), with µ m = λ 2 m , the mth eigenvalue. So, for each subinterval…”

Section: Generalized Fourier Transformmentioning

confidence: 99%

“…Generalized Fourier transforms have been studied by, e.g., [7][8][9][10][11]. More information is also available from [12][13][14][15][16]. Many results for steady and some transient N -layer systems with no explicit dependence on the vertical variable have been published by Bruggeman [17, pp.…”

Section: Introductionmentioning

confidence: 99%

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Strategy for solving semi-analytically three-dimensional transient flow in a coupled N-layer aquifer system

Veling

Maas

2008

J Eng Math

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Efficient strategies for solving semi-analytically the transient groundwater head in a coupled N -layer aquifer system φ i (r, z, t), i = 1, . . . , N , with radial symmetry, with full z-dependency, and partially penetrating wells are presented. Aquitards are treated as aquifers with their own horizontal and vertical permeabilities. Since the vertical direction is fully taken into account, there is no need to pose the Dupuit assumption, i.e., that the flow is mainly horizontal. To solve this problem, integral transforms will be employed: the Laplace transform for the t-variable (with transform parameter p), the Hankel transform for the r -variable (with transform parameter α) and a particular form of a generalized Fourier transform for the vertical direction z with an infinite set of eigenvalues λ 2 m (with the discrete index m). It is possible to solve this problem in the form of a semi-analytical solution in the sense that an analytical expression in terms of the variables r and z, transform parameter p, and eigenvalues λ 2 m ( p) of the generalized Fourier transform can be given or in terms of the variables z and t, transform parameter α, and eigenvalues λ 2 m (α). The calculation of the eigenvalues λ 2 m and the inversion of these transformed solutions can only be done numerically. In this context the application of the generalized Fourier transform is novel. By means of this generalized Fourier transform, transient problems with horizontal symmetries other than radial can be treated as well. The notion of analytical solution versus numerical solution is discussed and a classification of analytical solutions is proposed in seven classes. The expressions found in this paper belong to Class 6, meaning that the transformed solutions are written in terms of eigenvalues which depend on one transform parameter (here p or α). Earlier solutions to the transient problem belong to Class 7, where the eigenvalues depend on two transform parameters. The theory is applied to three examples.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…. is the mth eigenfunction of the generalized eigenvalue problem defined by (13)(14)(15), with µ m = λ 2 m , the mth eigenvalue. So, for each subinterval…”

Section: Generalized Fourier Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strategy for solving semi-analytically three-dimensional transient flow in a coupled N-layer aquifer system

Veling

Maas

2008

J Eng Math

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“…Using discrete kernel approach, Mishra et al (1985) [27] analyzed the two-aquifer system. Analytical solutions developed for multi-aquifers in general catered more to evoke the aquifer diffusivity ratios (Sokol, 1963;Wikramaratna, 1984;Hemker, 1984;Hunt,1985) [34], [38], [14], [17].…”

mentioning

confidence: 99%

Multi-Aquifer Parameterization with well loss in Vertical Flows

Majumdar¹

2015

JWRHE

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Abstract-Usually aquifer parameters are estimated through pumping/recharge test. Precondition for using those parameters in the numerical model is to ensure the synonymy of the hydro-geological condition between the field setup and the conceptual model. In many cases, it is erroneous. While numerical modelling in multi-aquifer considered vertical flow in general, it was reflected in the pumping solutions only to the extent of treating a leakage through the aquitard. As such well characterisation in multi aquifers separated by an aquiclude is illusive in the literature. As a result of which, interconnected aquifers were considered as isolated ones in the pumping/recharge tests. Therefore, estimated parameters were for a single aquifer, not for an aquifer connected to multi aquifers. In the present paper, the solution for a multi-aquifer system comprising of two interconnected aquifers separated by an aquiclude is presented. Vertical flow in the well bore with well loss due to friction has been considered. It is concluded that multi-aquifer parameters computed using present solution technique are more scientific and economical.

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A new formulation for steady multiaquifer flow: An analytic element for piecewise constant infiltration

Strack

Namazi

2014

Water Resources Research

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This paper contains a new formulation for infiltration inside domains bounded by polygons and its application to problems of steady multiaquifer flow, using the Dupuit-Forchheimer approximation and assuming vertical flow in the separating layers. An alternative formulation is presented for leaky aquifer systems where infiltration or extraction is given. Existing formulations of multiaquifer flow involve a system of equations that must be solved for the heads in the aquifers. These formulations are abstract, and the relation between the parameters in the solution and physical quantities is hidden. The formulation in the paper aims at linking the system of equations to physical quantities; we have done this in two ways. First, we formulate the problem in terms of leakage potentials, related directly to the leakage through the leaky layers. Second, we introduce the concept of ''equilibrated leakage,'' leakage that is either the result of infiltration or of some disturbance in the flow pattern, such as that caused by a well. The leakage through the leaky layers tends to some constant value far from a disturbance, e.g., a well, or the boundary of an area of constant infiltration. This concept of equilibrated leakage is useful in practice and helps in understanding the distribution of leakage; we explain this in detail in the paper. The study of problems of steady flow in leaky aquifer systems is inspired by problems of groundwater sustainability, where the overall distribution of flow over long periods of time is important, rather than detailed information.

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Steady groundwater flow in leaky multiple-aquifer systems

Cited by 57 publications

References 6 publications

Strategy for solving semi-analytically three-dimensional transient flow in a coupled N-layer aquifer system

Strategy for solving semi-analytically three-dimensional transient flow in a coupled N-layer aquifer system

Multi-Aquifer Parameterization with well loss in Vertical Flows

A new formulation for steady multiaquifer flow: An analytic element for piecewise constant infiltration

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