An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin

Chang, Chien-Chieh; Chen, Chia-Shyun

doi:10.1029/2001wr001091

Cited by 39 publications

(28 citation statements)

References 34 publications

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“…The general hydraulics of partially penetrating wells was assessed by e.g. Hantush (1957Hantush ( , 1961a, Kirkham (1959), Dougherty and Babu (1984), Ruud and Kabala (1997); Cassiani and Kabala (1998);Cassiani et al (1999), Chang and Chen (2002) and Yang and Yeh (2012). Kozeny (1933) derived an equation that allows assessing the head loss effect of partial penetration s pp in a homogeneous aquifer at steady state (Kasenow 2010).…”

Section: Effect Of Partial Penetrationmentioning

confidence: 99%

述评:水井水力学—水流定律和几何学的影响

Houben

2015

Hydrogeol J

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Water wells are an indispensable tool for groundwater extraction. The analytical and empirical approaches available to describe the flow of groundwater towards a well are summarized. Such flow involves a strong velocity increase, especially close to the well. The linear laminar Darcy approach is, therefore, not fully applicable in well hydraulics, as inertial and turbulent flow components occur close to and inside the well, respectively. For common well set-ups and hydraulic parameters, flow in the aquifer is linear laminar, non-linear laminar in the gravel pack, and turbulent in the screen and the well interior. The most commonly used parameter of well design is the entrance velocity. There is, however, considerable debate about which value from the literature should be used. The easiest way to control entrance velocity involves the well geometry. The influence of the diameter of the screen and borehole is smaller than that of the screen length. Minimizing partial penetration can help to curb head losses.

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Section: Effect Of Partial Penetrationmentioning

confidence: 99%

述评:水井水力学—水流定律和几何学的影响

Houben

2015

Hydrogeol J

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“…7. Hence, an intensive grid resolution is required in the vicinity of r = a (Cassiani et al 1999;Chang and Chen 2002;Mathias and Butler 2007). In addition, the domain has to be sufficiently large to faithfully represent the boundary conditions at r = ∞ and z = ∞.…”

Section: Numerical Solutionmentioning

confidence: 99%

Hydraulic Fracture Propagation with 3-D Leak-off

Mathias

Reeuwijk

2009

Transp Porous Med

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Hydraulic fracture models typically couple a fracture elasticity model with a geological reservoir model to forecast the rate of fluid leak-off from the propagating fracture. The most commonly used leak-off model is that originally specified by Carter, which involves the assumption that the fracture is embedded within an infinite homogenous porous medium where flow only occurs perpendicular to the fracture plane. The objectives of this paper are:(1) to show that assuming one-dimensional leak-off can lead to erroneous conclusions, (2) to present a robust numerical methodology for simulating three-dimensional leak-off from propagating hydraulic fractures, and (3) to present and compare a new analytical method based on assuming three-dimensional flow of an incompressible fluid through an incompressible porous formation from a circular planar fracture. Provided the fluid and formation compressibility can be ignored within the reservoir flow model, the three-dimensional leakoff from a circular planar fracture can be written in closed-form as a function, which depends linearly on fracture pressure and radial extent. This simple expression for leak-off can be easily coupled to a range of circular fracture elasticity models. As a comparison example, the Carter model, our new function and a three-dimensional numerical model of the full problem are coupled to the PK-radial fracture model. Comparison with the numerical model shows that our new function overestimates fracture growth during intermediate times but accurately predicts both the early and late-time asymptotic behavior. In contrast, the Carter model fails to replicate both the early and late-time asymptotic behavior. Our new function additionally improves on the Carter model by not requiring the evaluation of convolution integrals and allowing easy evaluation of both the spatial leakage flux distribution across the fracture face and the three-dimensional pressure distribution within the porous formation. List of symbolsa Radius of hydraulic fracture [L] a D = a/a f Dimensionless radius of hydraulic fracture [-] a f = {[E/(1 − ν 2 )](Qt f ) 2 /G} 1/5 Characteristic fracture radius [L] E Young's modulus [ML −1 T −2 ] G = K 2 Ic /E Specific surface energy of the rock [MT −1 ] k = (k r k z ) 1/2 Mean permeability [L 2 ] k r Permeability in r -direction [L 2 ] k z Permeability in z-direction [L 2 ] K Bulk modulus [ML −1 T −2 ] K Ic Critical mode I stress intensity factor [ML −1/2 T −2 ] M Biot modulus [ML −1 T −2 ] P Hydraulic pressure [ML −1 T −2 ] P d Hydraulic pressure within the fracture [ML −1 T −2 ] P dD = P d /P f Dimensionless hydraulic pressure within the fracture [-]Radial distance parallel to the fracture plane [L] r D = r/a f Dimensionless radial distance parallel to the fracture planeQt f Dimensionless volume of fracture [-] z Distance perpendicular to the fracture plane [L] z = (k r /k z ) 1/2 z Re-scaled distance perpendicular to the fracture plane [L] z D = z/a f Dimensionless distance perpendicular to the fracture plane [-] α Biot effective stress coef...

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“…The well skin is usually developed outside the wellbore because of the well construction (Novakowski 1989;Park and Zhan 2002;Chang and Chen 2002;Yeh and Yang 2006;Yeh and Chang 2013;Houben 2015b). In general, the well skin can be classified into two types, the infinitesimal skin and finite thickness skin.…”

Section: Introductionmentioning

confidence: 99%

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

Feng

Wen

2016

Hydrogeol J

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Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed nonDarcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index (n), the length of well screen (w), the apparent radial hydraulic conductivity of the formation zone (K r2 ), and the specific storage of the formation zone (S s2 ) at early times, and it is very sensitive to the parameters n, w and K r2 at late times, especially to n, while it is not sensitive to the skin thickness (r s ).

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An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin

Cited by 39 publications

References 34 publications

述评:水井水力学—水流定律和几何学的影响

述评:水井水力学—水流定律和几何学的影响

Hydraulic Fracture Propagation with 3-D Leak-off

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

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