Unsteady seepage flow between fully-penetrating trenches

Karadi, Gabor M.; Krizek, Raymond J.; Elnaggar, H A

doi:10.1016/0022-1694(68)90059-0

Cited by 8 publications

(3 citation statements)

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“…The coupled nonlinear algebraic equations describing contaminant transport can be avoided by stepwise solution of (1) and (3). Furthermore, many nonlinearities in groundwater simulation can be handled efficiently by commonly used linearization procedures such as predictor-corrector [Douglas and Jones, 1963] for unsaturated flow problems [Rubin, 1968] and ion exchange problems [Rubin and James, 1973], as well as the Runge-Kutta method for problems of unsteady seepage [Karadi et al, 1968]. In addition there are methods such as quasilinearization [Lee, 1968], and Gauss-Newton [Settari and Aziz, 1975] for strongly nonlinear problems.…”

Section: With Optimization Methodsmentioning

confidence: 99%

Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing

Gorelick¹,

Voss²,

Gill³

et al. 1984

Water Resources Research

253

141

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A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. Restrictions can be placed on hydraulic heads, stresses, and gradients, in addition to contaminant concentrations and fluxes. These restrictions can be distributed over space and time. Three design strategies are demonstrated for an aquifer that is polluted by a constant contaminant source: they are pumping for contaminant removal, water injection for in-ground dilution, and a pumping, treatment, and injection cycle. A transient model designs either contaminant plume interception or in-ground dilution so that water quality standards are met. The method is not limited to these cases. It is generally applicable to the optimization of many types of distributed parameter systems. This paper is not subject to U.S. copyright. Published in 1984 by the American Geophysical Union.Paper number 3W1963. the three categories of alternatives for remedial action as physical containment, in situ aquifer rehabilitation, and withdrawal followed by treatment and use. Physical containment systems prevent the flow of contaminated groundwater with the aid of engineered features such as slurry trench cutoff walls, grout curtains, and hydrodynamic controls. Aquifer rehabilitation methods may involve injection and recharge systems that are supplemented by above-ground chemical-treatment or may involve injecting a neutralizing or biochemical degradation agent into the contaminated zone. The approach of withdrawal, treatment, and use does not attempt to exploit any assimilative capacity or attenuation properties of the aquifer and simply removes the contaminated water from the system. Chemical treatment processes and waste containment for aquifer decontamination have been discussed by Landon and SylVester [1982], Yaniga [1982] for hydrocarbon contamination, Stover [1982], McBride [1982], and Ohneck and Gardner [1982] for removal of toxic organic chemicals, Osiensky et al. [1982] for uranium tailings disposal problems, and Molsather and Barr [1982], as well as Giddings [1982] for landfill leachate containment. . Aquifer management research has also treated the problem of groundwater pollution control. Remson and Gorelick [1980]considered the optimal locations of pumping and injection wells and the determination of minimum pumping rates for the hydraulic containment of contaminated groundwater. Their approach was to include the finite difference approximation of the groundwater flow equation as constraints in a linear programing problem. Further constraints served to control hydraulic gradients which prevented the plume from spreading as well as ...

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Section: With Optimization Methodsmentioning

confidence: 99%

Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing

Gorelick¹,

Voss²,

Gill³

et al. 1984

Water Resources Research

253

141

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“…Karadi et al ( 1968) [68] considered the problem of unsteady seepage flow (Figure 4) under the assumption that the porous medium is homogeneous and isotropic. Experimental data were obtained from a sand model with the following boundary and initial conditions:…”

Section: The Case By Karadi [68]mentioning

confidence: 99%

“…For t > 0 the water table is falling, and outflow volume is flowing to the two drains. Karadi et al (1968) [68] used a numerical solution, and the continuous domain is replaced by a pattern of discrete points, while the partial differential equation is replaced by a system of ordinary differential difference equations. An iteration process is used in order to obtain a small error in each time step.…”

Section: The Case By Karadi [68]mentioning

confidence: 99%

Fuzzy Finite Elements Solution Describing Recession Flow in Unconfined Aquifers

Tzimopoulos,

Papadopoulos,

Samarinas

et al. 2024

Hydrology

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In this work, a novel fuzzy FEM (Finite Elements Method) numerical solution describing the recession flow in unconfined aquifers is proposed. In general, recession flow and drainage problems can be described by the nonlinear Boussinesq equation, while the introduced hydraulic parameters (Conductivity K and Porosity S) present significant uncertainties for various reasons (e.g., spatial distribution, human errors, etc.). Considering the general lack of in situ measurements for these parameters as well as the certain spatial variability that they present in field scales, a fuzzy approach was adopted to include the problem uncertainties and cover the disadvantage of ground truth missing data. The overall problem is encountered with a new approximate fuzzy FEM numerical solution, leading to a system of crisp boundary value problems. To prove the validity and efficiency of the new fuzzy FEM, a comparative analysis between the proposed approach and other well-known and tested approximations was carried out. According to the results, the proposed FEM numerical solution agrees with Karadinumerical method for the crisp case and is in close agreement with the original analytical solution proposed by Boussinesq in 1904 with the absolute reduced error to be 4.6‰. Additionally, the possibility theory is applied, enabling the engineers and designers of irrigation, drainage, and water resources projects to gain knowledge of hydraulic properties (e.g., water level, outflow volume) and make the right decisions for rational and productive engineering studies.

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Comment on paper “Unsteady seepage flow between fully-penetrating trenches”

Venetis

1969

Journal of Hydrology

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Unsteady seepage flow between fully-penetrating trenches

Cited by 8 publications

References 0 publications

Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing

Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing

Fuzzy Finite Elements Solution Describing Recession Flow in Unconfined Aquifers

Comment on paper “Unsteady seepage flow between fully-penetrating trenches”

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