Stream depletion rate with horizontal or slanted wells in confined aquifers near a stream

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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“…Recently, Tsou et al . [] presented analytical solutions for flow into horizontal wells in a confined aquifer near a stream.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Zhan

2017

Water Resources Research

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“…Furthermore, they indicated that their solution can reduce to that of Zhan and Zlotnik [81] for the aquifer of infinitely horizontal extent. Most of studies in fact introduce this assumption to describe the flux to the horizontal well [84,117,240]. The second assumption for specifying the boundary along the horizontal well screens is the constant-head condition.…”

Section: Analytical and Semi-analytical Methodsmentioning

confidence: 99%

“…Generally, the governing equation describing the transient groundwater flow after taking the Fourier transforms reduces to an initial value problem. Applications of these transforms can be found, for example, in Tsou et al [84] who used exponential Fourier, Fourier sine, and finite Fourier cosine transforms to solve a 3-D groundwater flow problem for a confined aquifer with a slanted well near a stream, in Huang et al [85] who applied exponential Fourier, Fourier sine, and Laplace transforms to obtain an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream, and in other literatures [10,86] employing the finite Fourier sine or cosine or both finite Fourier sine and cosine transforms to solve a variety of groundwater flow problems.…”

Section: Fourier Transformmentioning

confidence: 96%

“…First, horizontal wells can be installed in aquifers where ground surfaces may have obstructions such as buildings and roads. Second, the use of horizontal wells yields smaller drawdown near the well than vertical ones do under the same pumping rate and well length [84]. Third, a horizontal well can generally extract more water than a vertical well does in shallow aquifers because the screen of horizontal wells is completely placed in the aquifer.…”

Section: Horizontal Wellmentioning

confidence: 99%

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Recent advances in modeling of well hydraulics

Yeh¹,

Chang²

2013

Advances in Water Resources

129

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“…The SDR ranges from zero to a certain value, which could be equal to or less than unity (Zlotnik, 2004). Tsou et al (2010) developed an analytical solution of the SDR for a slanted well in confined aquifers adjacent to a stream treated as a constanthead boundary. They indicated that a horizontal well parallel to the stream induces the steady-state SDR of unity more quickly than a slanted well.…”

Section: C-s Huang Et Al: Approximate Analysis Of Three-dimensionamentioning

confidence: 99%

Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

Huang

Chen

Yeh

2016

Hydrol. Earth Syst. Sci.

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Abstract. This study develops a three-dimensional (3-D) mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The streams with low-permeability streambeds fully penetrate the aquifer. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. Robin boundary conditions are adopted to describe fluxes across the streambeds. The head solution for the point sink is derived by applying the methods of finite integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy's law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length, and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow for the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.

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Stream depletion rate with horizontal or slanted wells in confined aquifers near a stream

Cited by 20 publications

References 25 publications

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

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

Recent advances in modeling of well hydraulics

Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

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