Analytical study of capture time to a horizontal well

Zhan, Hongbin

doi:10.1016/s0022-1694(99)00013-x

Cited by 58 publications

(35 citation statements)

References 11 publications

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“…Models have been used to investigate transient and steady drawdown near horizontal wells [e.g., Hantush and Papadopulos, 1962; Goode and Thambynayagam, 1987]. The geometry of capture zones for horizontal wells has been illustrated [Schafer, 1996;Steward, 1999;Zhan, 1999] Lieuallen-Dulam, 1998; Steward, 1999]. While the optimal well configurations in these publications differ, all conclude that horizontal wells are more effective than vertical wells at capturing contaminated groundwater.…”

Section: Introductionmentioning

confidence: 99%

“…Many models of horizontal wells assume that the flux (discharge removed from the aquifer per unit length along the well) is uniformly distributed along the well [e.g., Hantush and Papadopulos, 1962;Cleveland, 1994;Schafer, 1996;Zhan, 1999]. This boundary condition of uniform flux results in a model where the well is composed of one gaining section (where water enters the well from the aquifer) or one losing section (where water exits the well).…”

Section: Introductionmentioning

confidence: 99%

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Gaining and losing sections of horizontal wells

Steward¹,

Jin²

2001

Water Resources Research

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Abstract. The flux along a horizontal well in uniform flow is examined using an analytic three-dimensional, steady model. Wells with uniform head and low pumping rates have gaining sections along which water enters the well and losing sections along which water exits. Such a well may provide a conduit for contaminated groundwater to be drawn into the well, conveyed a large distance, and injected into an uncontaminated region of an aquifer. Dimensionless ratios of the well's length L and radius R, aquifer thickness H, and uniform flow rate U are developed to quantify the minimum pumping rate Q min at which no losing section occurs. The ratio Qmin/(ULH) is presented as a nomograph using R/H and L/H for placement parallel to flow and is 6rrR/H for placement perpendicular to flow, and a parabolic relationship between these limiting cases is developed for placement oblique to flow. Capture zone geometry is quantified using Qmin/(ULH).

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gaining and losing sections of horizontal wells

Steward¹,

Jin²

2001

Water Resources Research

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“…Hypothetical image wells were used to deal with the effects of the top and bottom boundaries. Zhan [1999] developed an analytical solution describing the capture time of a particle from its initial position to a horizontal well in a confined aquifer. Anderson [2000] derived an analytical solution of potential and stream functions for a horizontal well in a two-layer aquifer where the top boundary is under the Dirichlet condition representing static water table.…”

Section: Introductionmentioning

confidence: 99%

Estimating stream filtration from a meandering stream under the Robin condition

Huang

Yeh

2015

Water Resources Research

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This study applies image well theory to estimate the stream depletion rate (SDR) due to pumping near a meandering stream with a clogged streambed treated as the Robin condition. The stream is considered as an irregular boundary represented by discrete nodes. Image wells are arranged along the stream and near those nodes. On the basis of the Theis (1935) solution and the principle of superposition, the solution for the aquifer drawdown subject to the stream can then be expressed as the sum of the Theis solution and a simple series representing the effect of those image wells. The discharge rates of the image wells are determined by solving a system of equations obtained by substituting the drawdown solution into the Robin condition. Quantitative criteria for assessing the applicability of the image well theory are provided. On the basis of the drawdown solution and Darcy's law, the analytical solution for SDR can then be obtained. A finite element solution is also developed to verify the SDR solution. Temporal SDR distributions predicted by both the analytical solution and finite element solution agree well over the entire period except at late time when the stream filtration rate approaches the pumping rate (i.e., SDR ffi 1). It is found that a meandering stream has a significant effect on SDR compared with a rectilinear one and the effect should be taken into account in estimating SDR.

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“…In addition, horizontal wells have better contact within the stratum and can be installed in aquifers of small thickness if a long screen length is required. Several previous studies associated with the use of horizontal wells are proposed in the fields of water resources and environmental engineering (e.g., Zhan, 1999;Zhan, 2002, 2003;Zhan and Park, 2003;Kompani-Zare et al, 2005). Zhan et al (2001) provided an analytical solution to describe flow toward a horizontal well in an anisotropic confined aquifer.…”

Section: Introductionmentioning

confidence: 99%

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

Tsou

Zhang

Yeh

et al. 2010

Hydrol. Earth Syst. Sci.

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Abstract. Pumping in a vertical well may produce a large drawdown cone near the well. In this paper, the solution is first developed for describing the groundwater flow associated with a point source in a confined aquifer near a stream. Based on the principle of superposition, analytical solutions for horizontal and slanted wells are then developed by integrating the point source solution along the well axis. The solutions can be simplified to quasi-steady solutions by neglecting the exponential terms to describe the late-time drawdown, which can provide useful information in designing horizontal well location and length. The direction of the well axis can be determined from the best SDR subject to the drawdown constraint. It is found that hydraulic conductivity in the direction perpendicular to the stream plays a crucial role in influencing the time required for reaching quasisteady SDR. In addition, the effects of the well length as well as the distance between the well and stream on the SDR are also examined.

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Analytical study of capture time to a horizontal well

Cited by 58 publications

References 11 publications

Gaining and losing sections of horizontal wells

Gaining and losing sections of horizontal wells

Estimating stream filtration from a meandering stream under the Robin condition

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

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