Laplace-transform analytic-element method for transient porous-media flow

Kuhlman, Kristopher L; Neuman, Shlomo P.

doi:10.1007/s10665-008-9251-1

Cited by 21 publications

(15 citation statements)

References 49 publications

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“…To calculate the contributions to F due to the line-sink we need the ''holomorphic matching'' X ls (Z) which is found from (19) with (15) and (17) as:…”

Section: Exact Flow Across a Poly-linementioning

confidence: 99%

“…The functions above were developed for flow in a semi-confined aquifer with leakage, but they can also be applied to transient groundwater flow in the framework of the Laplace-Transform Analytic Element Method (LT-AEM) [14,15,20]. Two dimensional transient groundwater flow is governed by the heat equation [2,3]: …”

Section: Implementation In the Laplace-transform Aemmentioning

confidence: 99%

“…Following Kuhlman and Neuman [15] we write a general time variant solution in the time domain as the following convolution integral ( [15] Eq. (4)):…”

Section: Implementation In the Laplace-transform Aemmentioning

confidence: 99%

“…Kuhlman [20] explains that general time behavior in the LT-AEM is far more flexible, accurate and straightforward, compared to the approach by Zaadnoordijk [21] and Strack and Zaadnoordijk [22] who developed solutions directly in the time domain. The latter approach leads to a repeated superposition in time of line-sinks with a step function strength in order to approximate the desired behavior in time.…”

Section: Implementation In the Laplace-transform Aemmentioning

confidence: 99%

“…Again, k is defined differently here than for the cases of semi-confined aquifer flow or unsaturated flow. Kuhlman and Neuman [15] presented a solution to transient flow for a line-sink in the LT-AEM that is based on Mathieu functions and is valid for all r/k. We applied our solution to the LT-AEM and show that its range for r/k is sufficient for covering the entire relevant time domain and has the benefit of allowing for the calculation of transient integrated flow across a polyline.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An exact solution for a constant-strength line-sink satisfying the modified Helmholtz equation for groundwater flow

Gusyev¹,

Haitjema²

2011

Advances in Water Resources

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“…To calculate the contributions to F due to the line-sink we need the ''holomorphic matching'' X ls (Z) which is found from (19) with (15) and (17) as:…”

Section: Exact Flow Across a Poly-linementioning

confidence: 99%

Section: Implementation In the Laplace-transform Aemmentioning

confidence: 99%

“…Following Kuhlman and Neuman [15] we write a general time variant solution in the time domain as the following convolution integral ( [15] Eq. (4)):…”

Section: Implementation In the Laplace-transform Aemmentioning

confidence: 99%

Section: Implementation In the Laplace-transform Aemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An exact solution for a constant-strength line-sink satisfying the modified Helmholtz equation for groundwater flow

Gusyev¹,

Haitjema²

2011

Advances in Water Resources

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Intrawellbore kinematic and frictional losses in a horizontal well in a bounded confined aquifer

Wang

Zhan

2017

Water Resources Research

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Horizontal drilling has become an appealing technology for water resource exploration or aquifer remediation in recent decades, due to decreasing operational cost and many technical advantages over vertical wells. However, many previous studies on flow into horizontal wells were based on the Uniform Flux Boundary Condition (UFBC), which does not reflect the physical processes of flow inside the well accurately. In this study, we investigated transient flow into a horizontal well in an anisotropic confined aquifer laterally bounded by two constant-head boundaries. Three types of boundary conditions were employed to treat the horizontal well, including UFBC, Uniform-Head Boundary Condition (UHBC), and Mixed-Type Boundary Condition (MTBC). The MTBC model considered both kinematic and frictional effects inside the horizontal well, in which the kinematic effect referred to the accelerational and fluid-inflow effects. A new solution of UFBC was derived by superimposing the point sink/source solutions along the axis of a horizontal well with a uniform flux distribution. New solutions of UHBC and MTBC were obtained by a hybrid analytical-numerical method, and an iterative method was proposed to determine the well discretization required for achieving sufficiently accurate results. This study showed that the differences among the UFBC, UHBC, and MTBC solutions were obvious near the well screen, decreased with distance from the well, and became negligible near the constant-head boundary. The relationship between the flow rate and the drawdown was nonlinear for the MTBC solution, while it was linear for the UFBC and UHBC solutions.

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A low‐dimensional hillslope‐based catchment model for layered groundwater flow

Broda

Larocque

Paniconi

et al. 2011

Hydrological Processes

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Abstract:Despite the strong interaction between surface and subsurface waters, groundwater flow representation is often oversimplified in hydrological models. For instance, the interplay between local or shallow aquifers and deeper regional-scale aquifers is typically neglected. In this work, a novel hillslope-based catchment model for the simulation of combined shallow and deep groundwater flow is presented. The model consists of the hillslope-storage Boussinesq (hsB) model representing shallow groundwater flow and an analytic element (AE) model representing deep regional groundwater flow. The component models are iteratively coupled via a leakage term based on Darcy's law, representing delayed recharge to the regional aquifer through a low conductivity layer. Simulations on synthetic single hillslopes and on a two-hillslope open-book catchment are presented, and the results are compared against a benchmark three-dimensional Richards equation model. The impact of hydraulic conductivity, hillslope plan geometry (uniform, convergent, divergent), and hillslope inclination (0.2%, 5%, and 30%) under drainage and recharge conditions are examined. On the single hillslopes, good matches for heads, hydrographs, and exchange fluxes are generally obtained, with the most significant differences in outflows and heads observed for the 30% slope and for hillslopes with convergent geometry. On the open-book catchment, cumulative outflows are overestimated by 1-4%. Heads in the confined and unconfined aquifers are adequately reproduced throughout the catchment, whereas exchange fluxes are found to be very sensitive to the hillslope drainable porosity. The new model is highly efficient computationally compared to the benchmark model. The coupled hsB/AE model represents an alternative to commonly used groundwater flow representations in hydrological models, of particular appeal when surface-subsurface exchanges, local aquifer-regional aquifer interactions, and low flows play a key role in a watershed's dynamics.

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Laplace-transform analytic-element method for transient porous-media flow

Cited by 21 publications

References 49 publications

An exact solution for a constant-strength line-sink satisfying the modified Helmholtz equation for groundwater flow

An exact solution for a constant-strength line-sink satisfying the modified Helmholtz equation for groundwater flow

Intrawellbore kinematic and frictional losses in a horizontal well in a bounded confined aquifer

A low‐dimensional hillslope‐based catchment model for layered groundwater flow

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