Drawdowns for Leaky‐Aquifer Flow with Storage in Finite‐Width Sink

Motz, Louis H.

doi:10.1061/(asce)0733-9437(1994)120:4(820)

Cited by 7 publications

(11 citation statements)

References 16 publications

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“…They are analogous to the solutions for radial flow to a fully penetrating well with negligible well storage situated in a leaky aquifer (Hantush & Jacob, 1955). Motz (1992Motz ( , 1994 derived one-dimensional models for transient drawdown caused by constant discharge from a confined or leaky aquifer to a finite-width sink with storage. These solutions are analogous to the solutions for radial flow to a fully penetrating well with well storage derived by Papadopulos & Cooper (1967) for a confined aquifer and by Lai & Su (1974) for a leaky aquifer.…”

Section: Introductionmentioning

confidence: 94%

“…The initial boundary value problem equations (l)-(4) was formulated by Motz, (1994) and, independently in a slightly different form, by Thorne (1993). Motz (1994, equation (11)) provided (in an equivalent form) the following solution in the Laplace domain:…”

Section: Transient Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Even though the results of Motz (1994) could possibly serve as a basis for developing such a methodology, they are flawed. First, Motz (1994) derived only the appropriate drain function in the Laplace domain; its form in the time domain is not yet known. Second, the Laplace transform of the dimensionless drain function provided by Motz (1994, equation (11)) has a cumbersome form that employs dimensional rather than nondimensional groupings of variables.…”

Section: Introductionmentioning

confidence: 99%

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Hydraulics of one- and two-dimensional flow fields in aquifers

Kabala

Thorne²

1997

Hydrological Sciences Journal

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New solutions in the Laplace and time domains are developed that describe the transient response of a leaky aquifer to constant and transient discharge into a fully or partially penetrating sink with storage, A parameter estimation procedure based on the Newton-Raphson algorithm is found to be robust in a synthetic example involving a pumping test of a large-diameter well situated in a leaky strip aquifer. The analytical solutions presented may find applications in describing water movement in strip aquifers, in aquifers discharging into channels or streams, or in thin laboratory tanks.

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Section: Introductionmentioning

confidence: 94%

Section: Transient Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hydraulics of one- and two-dimensional flow fields in aquifers

Kabala

Thorne²

1997

Hydrological Sciences Journal

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“…In the case of underground flow applications [14][15][16], this is due to abrupt production rate changes. In compartmental modeling of pharmacokinetics [17][18][19][20] the phenomenon is related to administering the drug, say, by intravenous injection at a specific time.…”

Section: Why Do We Need New Sets Of Test Problems?mentioning

confidence: 99%

Inversion of Noise-Free Laplace Transforms: Towards a Standardized Set of Test Problems

Valkó

Vajda

2002

Inverse Problems in Engineering

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The numerical inversion of Laplace transform arises in many applications of science and engineering whenever ordinary and partial differential equations or integral equations are solved. The increasing number of available numerical methods and computer codes has generated a need for well-documented sets of test problems. Using such sets, algorithm developers can evaluate the relative merits and drawbacks of their suggested new methods, and end-users can make judgments on the applicability of an individual method for a specific problem. Many areas in science and engineering, lead to problems that share three important properties: (i) the image function can be evaluated for real arguments, but not necessarily for complex ones; (ii) the original is known to be infinitely differentiable for times t > 0, (iii) the values of the image function can be obtained with any prescribed accuracy. The published test sets do not properly cover these applications, as many included problems are beyond of the specific class, while the remaining ones fail to address some of the potential difficulties arising in practice. The goal of this paper is to establish a common ground for problem classification, to list the requirements for the above class of problems, and to provide a carefully selected test set by addressing the deficiencies of the ones currently available. The findings of the paper are used to solve a problem of practical importance in modeling underground flow. Accompanying the paper, WEB links are provided to a list of more than 800 relevant publications (going back to 1795), to a Mathematica program to generate and solve the suggested set of test problems, and to a user friendly Java program to solve inversion problems for a restricted class of image functions.

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