Contribution to head loss by partial penetration and well completion: implications for dewatering and artificial recharge wells

Abstract

A wide variety of well drilling techniques and well completion methods is used in the installation of dewatering and artificial recharge wells for the purpose of construction dewatering. The selection of the optimal well type is always a trade-off between the overall costs of well completion and development, the optimal well hydraulics of the well itself, the hydraulic impact of the well on its surroundings, and the required operational life span of the well. The present study provides an analytical framework that can be used by dewatering and drilling companies to quantify the contribution to head loss of typical dewatering and artificial-recharge well configurations. The analysis shows that the placement of partially penetrating wells in high-permeability layers could promote the use of quick and cheap installation of naturally developed wells using jetting or straight-flush rotary drilling. In high-permeability layers, such wells can be favorable over wells completed with filter pack, which require extensive well development to remove the fines from the filter cake layer. The amount of total head loss during discharge/recharge at a volumetric rate of 20 m3/h per meter of filter length, into or from a gravely aquifer layer, is reduced by factors of 3–4 while using naturally developed well types instead of well types completed with a filter pack that contains a filter cake layer due to borehole smearing.

Full text

PAPER
Contribution to head loss by partial penetration and well completion:
implications for dewatering and artificial recharge wells
J. H. van Lopik
1,2
&Thomas Sweijen
1,3
&N. Hartog
1,2
&R. J. Schotting
1
Received: 6 December 2019 /Accepted: 11 August 2020
#Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract
A wide variety of well drilling techniques and well completion methods is used in the installation of dewatering and artificial
recharge wells for the purpose of construction dewatering. The selection ofthe optimal well type is alwaysa trade-off between the
overall costs of well completion and development, the optimal well hydraulics of the well itself, the hydraulic impact of the well
on its surroundings, and the required operational life span of the well. The present study provides an analytical framework that
can be used by dewatering and drilling companies to quantify the contribution to head loss of typical dewatering and artificial-
recharge well configurations. The analysis shows that the placement of partially penetrating wells in high-permeability layers
could promote the use of quick and cheap installation of naturally developed wells using jetting or straight-flush rotarydrilling. In
high-permeability layers, such wells can be favorable over wells completed with filter pack, which require extensive well
development to remove the fines from the filter cake layer. The amount of total head loss during discharge/recharge at a
volumetric rate of 20 m
3
/h per meter of filter length, into or from a gravely aquifer layer, is reduced by factors of 3–4while
using naturally developed well types instead of well types completed with a filter pack that contains a filter cake layer due to
borehole smearing.
Keywords Well enhancement .Well completion .Head loss .Injection wells .Construction dewatering
Introduction
In order to obtain an optimal, energy-efficient well design,
thorough understanding of the well hydraulics is required to
minimize head losses during abstraction or recharge of water
from or into the subsurface (Driscoll 1986; Barker and Herbert
1992;Houben2015a,b). For a properly designed and devel-
oped water well, the largest head loss occurs in the aquifer
material (Powers et al. 2007;Houben2015b).
To date, most studies have investigated the efficiency of
abstraction wells for freshwater supply (e.g. Driscoll 1986;De
Zwart 2007; Van Beek et al. 2009a,b; Houben 2015a,b;
Houben et al. 2018). These studies focus on typical well de-
signs for drinking water wells (Barker and Herbert 1992;
Houben 2015b), as well as the well efficiency reduction over
time by mechanical or chemical clogging (e.g. De Zwart
2007; Van Beek et al. 2009a,b; Houben et al. 2018).
Drinking water wells are designed to operate for decades,
and hence high costs of proper extensive well development
and completion usually overcome the additional pumping
costs of cheaper but poorly developed and completed abstrac-
tion wells. Typically, such wells are screened over a large
portion over the aquifer in order to reduce additional head loss
by partial penetration.
However, for many water well applications, partially pen-
etrating wells (PPWs) are unavoidable to optimize the entire
well-system. Water well systems such as combined
dewatering and artificial recharge systems at construction sites
(Powers et al. 2007;VanLopik2020; Van Lopik et al. 2020a),
aquifer storage and recovery (ASR) systems (Zuurbier et al.
2014), and high temperature aquifer thermal energy storage
(HT-ATES) systems (Buscheck et al. 1983; Van Lopik 2020),
can be improved with PPWs that target specific portions of the
aquifer. During construction dewatering, PPWs (deep-wells
or vacuum point-wells) are screened at the required drawdown
*J. H. van Lopik
jan.van.lopik@kwrwater.nl
1
Department of Earth Sciences, Utrecht University, Princetonlaan 8,
3584, CB Utrecht, The Netherlands
2
KWR Water Research Institute, Geohydrology, Groningenhaven 7,
3433, PE Nieuwegein, The Netherlands
3
CRUX Engineering BV, Pedro de Medinalaan 3c, 1086, XK
Amsterdam, The Netherlands
Hydrogeology Journal
https://doi.org/10.1007/s10040-020-02228-5

depth to obtain the desired groundwater levels at the construc-
tion site. The installation of such dewatering PPWs require
less drilling and completion costs compared to wells that
screen a large portion of the aquifer. For combined well sys-
tems of dewatering wells and artificial recharge wells to
reinfiltrate the pumped groundwater in the target aquifer,
dewatering companies in the Netherlands and Germany have
started to use recharge PPWs to minimize the hydraulic im-
pact at shallow subsurface levels during construction
dewatering (see Van Lopik et al. 2020a). Often, such PPWs
are naturally developed (installed without filter pack) and
placed with quick, relatively cheap drilling methods such as
jetting or straight-flush rotary to save the costs of the entire
dewatering scheme for an excavation. Consequently, the well
hydraulics of such artificial recharge wells differ significantly
from conventional artificial recharge wells.
Particularly for dewatering at construction sites, a wide
range of well completion methods are used to install
dewatering wells (e.g. deep wells or vacuum points wells)
to lower the water table and, optionally, artificial recharge
wells to reinject water into the aquifer. The selected type of
well completion of such water wells largely determines the
entire efficiency of the dewatering system (Powers et al.
2007; Cashman and Preene 2013). Therefore, the efficien-
cies of the various abstraction and artificial recharge well-
types in construction dewatering are critical to reduce the
pumping costs and overall carbon footprint during the
dewatering operation. Dewatering companies have the op-
portunity to select from a wide range of drilling techniques
to install the most suitable, least-expensive well-type based
on the extent and operational time of the dewatering sys-
tem. In general, the operational life-span of a dewatering
abstraction or artificial recharge well is significantly lower
than in other well applications. Hence, the costs and time of
proper well completion and development need to be bal-
anced with the overall pumping costs for a specific
dewatering application.
During artificial recharge and abstraction, the effect of ad-
ditional head losses by non-linear flow behaviour in the filter
pack, as well as in the aquifer material, can be significant due
to increased flow velocities by diverging/converging flow
lines in the vicinity of wells (e.g. Basak 1978, Barker and
Herbert 1992;Houben2015a,b). In the initial stage of well
operation of properly designed and developed drinking water
wells in sandy aquifers, hardly any effect of nonlinear flow
behaviour is observed (<4% of additional head loss; Barker
and Herbert 1992; Houben 2015b). However, during well
operation, clogging of abstraction and injection wells can
cause additional head losses (Olsthoorn 1982;DeZwart
2007; Van Beek et al. 2009a,b;Powersetal.2007;Martin
2013;Houbenetal.2018). Severe clogging of wells could
result in reduced porosity in the filter pack and drastic increase
of nonlinear flow behaviour (Houben et al. 2018).
In the present study, the important aspects of well hydrau-
lics of typical well-types used for construction dewatering are
investigated using analytical equations. To date, the well spec-
ification of such wells are generally based on the equipment
and expertise of the drilling or dewatering company (Powers
et al. 2007; Cashman and Preene 2013). Existing literature
focusses on the well hydraulics of typical drinking water well
types that are completed with a proper filter pack (e.g. Barker
and Herbert 1992; Houben 2015a,b). However, the well hy-
draulics of naturally developed wells used in construction
dewatering, which are installed with cheap, quick well com-
pletion methods such as jetting and straight-flush rotary dril-
ling, differs from typical drinking water wells (e.g. Powers
et al. 2007; Van Lopik 2020). In order to compare the well
efficiency of naturally developed wells and proper completed
wells with a filter pack screened in different kinds of aquifer
types (ranging from sand to gravel), the contributors of the
individual head components to the total head loss outside the
well screen are evaluated in the present study. This is done by
using actual hydraulic properties for a broad range of filter
sands and natural sand and gravel deposits from aquifers that
include the nonlinear flow behaviour characteristics obtained
from experimental datasets (Van Lopik et al. 2017,2020b).
Besides the wide variety in well completion methods used in
construction dewatering, the effect of partial penetration on
well efficiency is investigated. Generally, additional head loss
of PPWs that only screen a small portion of the aquifer results
in large additional head losses (e.g. Barker and Herbert 1992;
Houben 2015a; Tügel et al. 2016). However, accounting for
the aquifer heterogeneity during PPW placement in high-
permeability strata of the aquifer, instead of considering ho-
mogeneous anisotropic conditions for the aquifer, might sig-
nificantly reduce additional head losses due to partial penetra-
tion. The current analytical analysis will provide insight to
what extent cheap installation of naturally developed wells,
as well as PPWs that only screen a small portion of the aquifer,
can be used at reasonable well efficiency during operation
compared to more costly well completion with a filter pack
and wells that screen a large portion of the aquifer for
dewatering purposes.
Theory
Well completion with various drilling techniques
In practice, a broad variety of well-types is available for
dewatering with deep wells or injection with artificial recharge
wells (Powers et al. 2007). The selection of the well-type (e.g.
borehole diameter, well diameter, filter screen, filter pack,
screen slot dimensions) depends on the pumped or injected
volumes, aquifer characteristics and operational life span of
the well. For example, relatively cheap PVC wells that need to
Hydrogeol J

be operative for a couple of weeks usually suffice for most
dewatering projects. Moreover, in practice, the expertise of
each specific dewatering company, as well as the availability
of specific drilling equipment, also largely determines well
design (especially for smaller dewatering projects).
In the present study, typical drilling and well completion
methods for dewatering and artificial recharge wells in uncon-
solidated soils used by the dewatering companies are consid-
ered. Two different well completion methods are investigated:
–Naturally developed wells assuming completion without
a filter pack with a larger borehole diameter than the well
diameter and a zone of aquifer collapse (well-types
WAC1–2, see Fig. 1a and Table 1).
–Well completion with a filter pack and filter cake (well-
types WFP1–2, see Fig. 1b and Table 1).
Aquifer collapse with no filter pack (naturally developed
wells)
In practice, manual jetting and straight-flush rotary drilling are
suitable methods for relatively cheap and quick installation of
dewatering and artificial recharge naturally developed wells
without artificial filter pack (Powers et al. 2007). Similar to
manual jetting, during mechanical drilling by straight-flush
rotary, a drilling-fluid is pumped down the drill-rod of the
drilling rig to flush out the debris mixture of water and soil.
A rotating drill-bit cuts and penetrates the soil. The velocity of
the drilling fluid in the borehole annulus must be sufficient to
lift the debris up to the surface level. Large quantities of the
flushed water volume pumped down the drill-pipe are infil-
trated into the surrounding soil during this drilling method
(Powers et al. 2007). Drilling through high-permeability
layers in the aquifer causes a significant loss of flushed water
volume into the surrounding soil and a sudden reduction in
debris flush velocity in the borehole annulus. This allows for
quick and cheap placement of partially-penetrating wells in
high-permeability strata in the aquifer without a filter pack
using straight-flush rotary or jetting (e.g. Van Lopik 2020).
Typical drilling fluids for jetting or straight-flush rotary dril-
ling techniques are water, bentonite-mud and polymeric drilling
fluids (Powers et al. 2007). If clean water is used as a drilling
fluid during uncased drilling methods such as jetting or straight-
flush rotary, the lack of filter cake formation results in an un-
stable borehole wall and hence, proper well completion with a
filter pack in sandy aquifers is difficult. Placement with jetting
Fig. 1 Head losses (blue line)
during artificial recharge in an
aquifer for aa naturally
developed well drilled with the
jetting or straight-flush rotary
drilling method considering aqui-
fer collapse (well-type with
aquifer collapse, WAC) and ba
well drilled with the reverse-
circulation rotary drilling method
considering filter pack and filter
cake with positive skin layer
(well-type with filter pack WFP).
In this figure, r
s
is the radius of the
screen, r
b
is the radius of the
borehole, r
sk-in
is the radius from
well centre to the inner boundary
of the skin layer, r
sk-out
is the ra-
dius from well centre to the outer
boundary of the skin layer, r
o
is
the radius of influence where head
increase is zero (h
0
). Also, the
components of head loss in the
aquifer material (Δh
aq
), collapsed
aquifer zone (Δh
AC
), filter pack
(Δh
fp
) and skin layer (Δh
sk
)are
shown
Hydrogeol J

of naturally developed dewatering well points without a filter
pack are common practice in sandy aquifers. In the last decade,
dewatering companies in the Netherlands and Germany started
to install naturally developed partial-penetrating artificial re-
charge wells using jetting or straight-flush rotary drilling with
clean water as drilling fluid (Van Lopik 2020). After proper
well development, such naturally developed wells could have
a negative well skin, due to improved hydraulic conductivities
in the vicinity of the well by easy mobilization of finer particles
during well development after jetting or straight-flush rotary
drilling with a clean drilling fluid, limited formation of filter-
cake, and aquifer collapse within the area between the well and
the outer borehole diameter after placement (r
s
<r<r
b
;
Driscoll 1986; Roscoe Moss Company 1990). Moreover, the
filter-cake that is formed due to precipitation of fines by the up-
flowing debris along the borehole collapses and mixes with the
aquifer material (Fig. 1a). Generally, the borehole radius of
jetting and straight-flush rotary drilled wells in stratified soils
is highly irregular. In the present study, the radius r
b
was used
as the outer radius of the negative skin zone with collapsed
aquifer material.
Stable borehole with filter pack
For prolonged recharge or dewatering purposes, reverse-
circulation rotary drilling is a widely used method for well
placement of deep wells or artificial recharge wells (Powers
et al. 2007). This method enables drilling of large diameter
boreholes, and hence large diameter wells can be placed while
allowing for proper completion with a filter pack. The drilling
method also uses a rotating drilling bit to penetrate and cut the
soil. However, the drilling fluid flows down the borehole out-
side the drill-rod and lifts the drilling fluid and soil to surface
level through the drill-rod by suction.
Usually, filter cake at the borehole surface is formed due to
precipitation of fines and drilling mud during well placement,
causing a small positive skin zone of low permeability. If the
well is properly designed and developed, the second-most
significant portion of the total additional well loss occurs in
this well skin (e.g. Houben 2015b; Houben et al. 2016).
Prolonged, costly well development procedures are required
to minimize the additional head loss due to well skin. Hence,
in practice, significant head loss often occurs due to the pos-
itive well skin in dewatering deep wells and artificial recharge
wells.
Nonlinear flow behaviour in porous media
Commonly, the Reynolds number (Re) is used to indicate
whether flow is in the laminar Darcian flow regime or in the
nonlinear flow regime (Bear 1988):
Re ¼d50q
vð1Þ
where v[m
2
/s] is the is the kinematic viscosity of the fluid and
d
50
[m] is the characteristic pore length by means of the me-
dian particle diameter. Most studies consider Reynolds num-
bers ranging from 1 to 10 for transition between laminar
Darcian flow and nonlinear flow (e.g. Bear 1988; Houben
2015a; Van Lopik et al. 2017,2020b). Nonlinear post-
Darcian flow behavior can be described by the alternative
flow law of Forchheimer (1901):
i¼−aq−bq2ð2Þ
where a[s/m] is a parameter equal to the reciprocal of the
hydraulic conductivity (i.e., a=1/K)andb[s
2
/m
2
] is the em-
pirical Forchheimer coefficient. Similar to the Kozeny-
Carman relationship, Ergun (1952) related the Forchheimer
coefficients to the grain size and porosity by:
i¼−A1−nðÞ
2v
gn3d2q−B1−nðÞ
gn3dq2ð3Þ
where g[m/s
2
] is the acceleration due to gravity, d[m] is the
characteristic pore length by means of the particle diameter, n
[−] is the porosity, Aand B[−] are the Ergun constants.
Table 1 Typical well configuration of artificial recharge wells used for
discharge into aquifers during dewatering (see Fig. 1). The configuration
of well-types WFP1 and WFP2 can also be used for deep wells in
dewatering systems. Drilling procedures are also given. These configura-
tions are used as reference to determine head losses during recharge or
abstraction. In this table, r
s
is the radius of the screen, r
b
is the radius of the
borehole, r
o
is the radius of influence where head increase is zero (h
0
) (see
Fig. 1), n
s
the number of slots inside the circumference of the well and w
s
is the slot aperture
Parameter Aquifer collapse with no filter pack Stable borehole with filter pack
WAC1 (jetting) WAC2 (straight-flush rotary) WFP1 (reverse-circulation rotary) WFP2 (reverse-circulation rotary)
r
0
[m] 500 500 500 500
r
b
[m] 0.04 0.1 0.2 0.25
r
s
[m] 0.03 0.055 0.1 0.15
n
s
[−] 32 60 100 150
w
s
[m] 0.0003 0.0003 0.0007 0.0007
Hydrogeol J

Natural sand and gravel deposits
A broad dataset of Forchheimer coefficients aand bfor gran-
ular material is found in the literature (e.g. Moutsopoulos et al.
2009; Van Lopik et al. 2017,2020b). Most studies provide
data related to uniformly graded material with coefficients of
uniformity (C
u
=d
60
/d
10
) smaller than 3. The study of Van
Lopik et al. (2020b) shows that for a wide range of grain size
distributions with C
u
> 3 and low porosity values, the amount
of fines (characteristic pore length of d
10
) can be used to pre-
dict the Forchheimer coefficients aand b. For the present
study, experimentally derived Forchheimer coefficients from
packed bed experiments on natural sands and gravel are used
(Table 2).
Filter packs
Usually, basic criteria for the selection of suitable filter packs
are provided in the literature for artificial recharge and
dewatering deep wells (Pyne 2005;Powersetal.2007).
Ideally, the used filter pack is based on the aquifer material,
and grain size analysis of the aquifer is required (Driscoll
1986; Roscoe Moss Company 1990; Powers et al. 2007):
–The filter pack is as coarse as possible. However, selec-
tion of filter packs with grain sizes that are too coarse
allows passing and migration of fines, from the aquifer
towards the well screen during abstraction. In highly strat-
ified soils, filter packs should be based on the finest strata.
During well development of artificial recharge wells, the
risk of mobilization of fines into the filter pack should be
taken into account and hence, selection of filter pack is
approximately similar to that of dewatering deep wells
(e.g. Powers et al. 2007).
–The filter material is uniformly graded (C
u
< 3). More
specifically, the filter pack should have a lower C
u
than
the aquifer material.
–The median grain size (d
50
) of the filter pack should be 4–
6 times higher than the aquifer material.
Due to high flow velocities (Re > 10) by converging or
diverging flow lines in the filter pack of respectively abstrac-
tion and recharge wells, head loss due to nonlinear flow be-
haviour occurs (e.g. Houben 2015a,b). Van Lopik et al.
(2017) investigated the nonlinear flow behaviour through
packed-bed experiments of typical filter pack sands and
gravels (with C
u
< 3). Five types of different filter pack mate-
rial were selected for this study, ranging from medium to very
coarse sand, in order to investigate the nonlinear flow head
losses in wells (Table 2). Filter pack porosities of 0.34–0.36
are realistic values for the packing density of filter packs of
dewatering wells (Houben et al. 2016).
Well hydraulics of artificial recharge and deep wells
The present study focusses on the different individual compo-
nents of head loss in the filter pack and aquifer for typical
artificial recharge wells and deep wells used by dewatering
companies invarious parts of the world. Inorder to investigate
the head losses during artificial recharge or groundwater ab-
straction in a confined aquifer by a vertical, fully penetrating
well, analytical equations are used to obtain a general over-
view for different well-types (see Houben 2015b). Typical
geometry and parameters for deep wells and artificial recharge
wells are used, see Table 1for specifications. In general, ad-
ditional head loss due to free flow in the well interior (well
casing and screen) and through the screen slots is very small
(Barker and Herbert 1992;Houben2015b). Hence, this study
solely focuses on the head losses outside the well screen.
Table 2 Typical hydraulic characteristics of different types of filter packs and aquifer material. Forchheimer coefficients aand bfor nonlinear flow
behaviour are obtained from packed-bed flow experiments (Van Lopik et al. 2017,2020b)
Material d
10
[mm]
d
50
[mm]
C
u
K
[m/day]
a
[s/m]
b
[s
2
/m
2
]
n
[−]
Filter pack
FP-MS1: medium sand 0.28 0.39 1.48 60.57 1,426.5 12,523 0.34
FP-CS1: coarse sand 0.53 0.71 1.42 153.7 562.16 6,781.8 0.34
FP-CS2: coarse sand 0.80 1.0 1.30 351.6 245.75 4,396.0 0.35
FP-VCS1: very coarse sand 1.16 1.5 1.36 823.0 104.98 2,497.9 0.36
FP-VCS2: very coarse sand 1.72 2.1 1.27 1,339 64.503 1,746.3 0.36
Aquifer material
A-CS1: coarse sand 0.29 0.77 3.86 53.58 1,612.5 14,464 0.33
A-VCS1: very coarse sand 0.46 1.5 4.84 65.15 1,326.1 36,662 0.25
A-CG1: coarse gravel 0.95 9.5 13.1 328.0 263.37 9,957.7 0.25
A-CG2: coarse gravel 1.36 6.3 7.35 527.3 163.84 6,186.8 0.25
Hydrogeol J

Darcian and non-Darcian flow towards a well
For classical abstraction or recharge wells that screen large
parts of the aquifer, flow is solely in the lateral direction and
radial-symmetric flow conditions can be assumed. Hence,
steady-state groundwater flow to and from such abstraction
or recharge wells in a fully confined homogeneous aquifer
can be described by Thiem’s equation (1870):
Δh¼Q
2πKH ln r2
r1
 ð4Þ
where Δh[m] is the head loss, Q[m
3
/s] is the volumetric well
discharge/recharge, H[m] is the aquifer thickness and r
1
and
r
2
[m] are the radial distances.
At high abstraction or injection flow velocities in the vicin-
ity of the well, Reynolds numbers are high (Re > 10) and
nonlinear flow behaviour could occur (e.g. Engelund 1953;
Basak 1978; Houben 2015a,b). The extended form of
Thiem’s equation can be used to account for nonlinear
Forchheimer flow head losses in the gravel pack or aquifer:
Δh¼Q
2πKH ln r2
r1

þbQ
2πH

21
r1
−1
r2
 ð5Þ
Flow convergence/divergence near screen slots
Close to the screen slots, the convergence or divergence of
flow lines to or from the screen slots causes an additional head
loss. The equation for flow line convergence/divergence by
Boulton 1947 (as cited by Houben 2015b)duringabstraction
or injection is verified and extended for both Darcian and
Forchheimer flow (see Appendix):
Δhdv ¼Q
2πnsKLs
ln 2
1−cos δsπðÞ

þb
rs
Q
2πnsLs

2
ð6Þ
where K[m/day] is the hydraulic conductivity, L
s
[m] is the
length of the screen (equals aquifer thickness in this study), n
s
[−] is the number of slots inside the circumference of the well,
r
s
[m] is the radius of the well screen and δ
s
[−] is the ratio of
slot aperture and circumference of the well.
This extended equation is applied for the component of
head loss due to flow convergence/divergence inthe collapsed
aquifer zone for well-types WAC1–2(Eq.7,inTable3), as
well as in the filter pack for well-types WFP1–2 (Eq. 10, in
Table 3).
Equations for individual components of head loss
Equation (5) is used to account for the individual components
of head loss in both the collapsed aquifer zone (Eq. 8) as well
as the aquifer itself (Eq. 9) for the well-types WAC1–2
(Table 3). Similarly, Eq. (5) is used to account for the individ-
ual components of head loss in both the filter pack (Eq. 11)
and the aquifer itself (Eq. 13) for the well-types WFP1–2. To
obtain a rough estimate of the additional head loss due to the
formation ofa filter cake(positive skin), the Thiem equation is
considered(Eq. 12).In general, the hydraulic conductivity and
thickness of the well skin is difficult to predict, since in-situ
samples are required to make proper estimates (Powers et al.
2007;Houben2015b;Houbenetal.2016). The present study
assumed a filter cake layer of 1 mm at r
b
(r
sk-in
<r<r
sk-out
)
with a hydraulic conductivity (K
sk
) of 1e-6 m/s, which are
reasonable values for water wells (Houben et al. 2016).
Methods
The different components of head losses for typical artificial
recharge and dewatering deep wells are estimated analytically
for four different kind of well-types (Table 1). In the present
study, the effects of nonlinear flow behaviour in well hydrau-
lics were investigated using the provided experimental
datasets on packed-bed flow experiments of filter sands
(Van Lopik et al. 2017) and natural sands (Van Lopik et al.
2020b;Table2). The impact on well hydraulics is investigated
for:
–The individual components of total head loss of the dif-
ferent well types in the different aquifer materials ranging
from coarse sand to coarse gravel (Table 2). The contri-
butions to the total head loss in the collapsed aquifer zone
(Δh
AC
) and aquifer (Δh
aq
) are investigated for well types
WAC1–2, as well as in the filter pack (Δh
fp
), skin (Δh
sk
)
and aquifer (Δh
aq
) for WFP1–2(Table3).
–The efficiency of the filter packs ranging from medium to
very coarse sand. These are investigated and compared to
ahypotheticalcasewithnofilterpack(assumingthechar-
acteristics of aquifer material within the borehole radius).
–The effect of well-clogging in the filter pack.
–The effect of additional head loss by partial penetration of
the well.
Individual components of total head losses in
different aquifer types
To calculate the individual components of head loss, the ana-
lytical equations listed in Table 3are used. For the well types
with filter pack (WFP1–2), completion with very coarse sand
(FP-VCS1 with K
fp
= 823 m/day) is considered. The associat-
ed hydraulic properties of the filter pack FP-VCS1 and the
aquifer materials are listed in Table 2.
For the collapsed aquifer zone around the well drilled by
jetting/straight-flush rotary methods (well types WAC1–2), an
Hydrogeol J

improved hydraulic conductivity which is two times lower
than the actual aquifer material is assumed. For estimation of
the reduced nonlinear flow resistance, coefficient bis estimat-
ed by: b=172.77a
0.548
(see Van Lopik et al. 2017).
Additional head loss in the filter pack
Selection of a suitable filter pack is essential for a proper well
completion. Ideally, the filter pack is selected such that the
flow resistance is lower than the aquifer material (see section
‘Filter packs’). Hence, in order to compare the efficiency of
different filter pack types with equivalent scenarios consider-
ing only aquifer material within the well bore zone, the addi-
tional head losses by laminar Darcy flow, nonlinear flow and
flow convergence/divergence to screen slots within the zone
of r
s
<r<r
b
are calculated for the sand types listed in Table 2.
Clogging of the filter pack
Clogging of water wells could occur inside the well interior,
screen slots and the filter pack (Olsthoorn 1982; De Zwart
2007; Van Beek et al. 2009a,b; Houben et al. 2018).
Usually, severe clogging of well screens and well interior by
biofouling of incrustation of dewatering deep wells or artifi-
cial recharge wells (Powers et al. 2007) can be reversed after
proper well development. However, well development does
not remove all clogging particles in the filter pack, at the
borehole wall, and in the aquifer itself (Houben et al. 2016,
2018). The most important factor in well clogging is the clog-
ging of the filter pack (Houben et al. 2018).
Therefore, similar to the Houben et al. (2018) study on
filter pack ageing of drinking water wells, the increase in head
losses due to porosity reduction in the filter pack is investigat-
ed for well-type WFP1 and the hydraulic properties of filter
and natural sand based on Van Lopik 2017 and 2020b.The
Ergun relation (Eq. 3) is used with the Ergun constants Aand
Bof respectively 233.5 and 2.88 and d
50
for filter pack clog-
ging. These values have shown representative prediction of
nonlinear flow behaviour through packed beds of various fil-
ter sands and gravels (Van Lopik et al. 2017). The effect of
reduced porosity values by clogging on the hydraulic conduc-
tivity and Forchheimer coefficient bis shown in Fig. 2for the
filter packs of medium sand (FP-MS1), coarse sand (FP-CS2)
and very coarse sand (FP-VCS2). Moreover, the effect of
porosity reduction by clogging of well-type WAC2 is shown,
considering the aquifer materials of A-VCS1 and A-CG1 in
Table 3 The different components of additional head losses for well types WAC1–2(seeFig.1a) and for well types WFP1–2(seeFig.1b)
Component Equation
Well types WAC1–2
Divergence flow (Eq. 7) Δhdv ¼Q
2πnsKACHln 2
1−cos δsπðÞ
hi
þbAC
rs
Q
2πnsH

2
Collapsed aquifer zone (Eq. 8) ΔhAC ¼Q
2πKACHln rb
rs
þbAC Q
2πH

21
rs−1
rb

Aquifer (Eq. 9) Δhaq ¼Q
2πKaqHln r0
rb
þbaq Q
2πH

21
rb−1
r0

Well types WFP1–2
Divergence flow (Eq. 10) Δhdv ¼Q
2πnsKfpHln 2
1−cos δsπðÞ
hi
þbfp
rs
Q
2πnsH

2
Filter pack (Eq. 11) Δhfp ¼Q
2πKfpHln rb
rs
þbQ
2πH

21
rs−1
rb

Positive skin layer (Eq. 12) Δhsk ¼Q
2πKskHln rsk−o
rsk−in

Aquifer (Eq. 13) Δhaq ¼Q
2πKaqHln r0
rb
þbaq Q
2πH

21
rb−1
r0

Parameter labels Individual components of head loss
aq Aquifer material
AC Material in zone of aquifer collapse
sk Skin layer
fp Filter pack
dv Flow divergence from screen slots
Well dimensions
s Wells screen
b Borehole wall
sk-in Inner boundary skin layer
sk-o Outer boundary skin layer
0 Radius of influence where head increase is zero (h
0
)
Hydrogeol J

the collapsed aquifer zone for a naturally developed well. For
these cases, the modified form of the Ergun relationship (Eq.
3) for natural sands is considered (Van Lopik et al. 2020b).
Hence, Ergun constants Aand Bof respectively 69.0and 1.85,
and the grain size of d
10
as a characteristic length scale, are
assumed to estimate the effects of porosity reduction by the
formation of a positive skin layer due to aquifer clogging (see
Fig. 2). In this study, the filter sands with hydraulic conduc-
tivities of 60.6 m/day (FP-MS1), 351 m/day (FP-CS1) and
1,339 m/day (FP-VCS2) are used as reference and tested for
additional head loss by well clogging.
Effect of partial penetration on additional head loss
In the aforementioned scenarios, axi-symmetric flow in solely
the lateral direction is considered using the Thiem equation,
which is valid when the Dupuit-Forchheimer approximation
holds, see Eqs. (4)and(5). However, well-types for
dewatering and artificial recharge at construction sites such
as given in Table 1are generally not fully screened over the
entire depth of the aquifer. Dewatering deep wells are placed
at depth for the required drawdown for construction. Artificial
recharge wells could be screened in deeper parts of the aquifer
to minimize hydraulic impact on the excavation site and
allowing for closer placement to the dewatered area (Van
Lopik et al. 2020a).
In order to estimate additional head loss by partial penetra-
tion compared to an equivalent scenario of full penetration
over the entire aquifer thickness, many equations have been
postulated (e.g. Barker and Herbert 1992; Kasenow 2010;
Houben 2015a). In the present study, the equation of Barker
and Herbert (1992) is used to account for anisotropic aquifer
conditions and determine analytically the impact of different
aquifer characteristics on head loss for PPWs. Additional head
losses by partial penetration of the well in a homogeneous,
anisotropic aquifer can be calculated by:
Δhpp ¼Q
2πKhH
1−pp
pp
ln
pp1−pp

2−ε2
H
rbffiffiffiffiffiffi
Kh
Kv
r
2
43
5ð14Þ
where K
h
[m/day] is the horizontal hydraulic conductivity, K
v
[m/day] is the vertical hydraulic conductivity, p
p
[−]isthe
partial penetration ratio between screen length and the aquifer
thickness (H) and ε[−] is the eccentricity of the well, de-
scribed by:
ε¼2zc
H1−pp
 ð15Þ
where z
c
[m] is the vertical distance between the middle of the
aquifer and the centre of the well screen. Note that Eq. (14)is
only applicable for Darcian flow conditions and p
p
ratios be-
tween 0.1 and 0.9. Considering nonlinear flow behaviour only
occurs in the near vicinity of the well (e.g. filter pack or col-
lapsed aquifer zone), this equation is valid to estimate addi-
tional head loss by partial penetration.
Generally, high-permeability layers in a given target aqui-
fer are selected in order to optimize the well design (Fig. 3a).
Often, poor aquifer characterization by a rough estimate of the
horizontal hydraulic conductivity and vertical hydraulic con-
ductivity based on an assumed anisotropy factor with typical
educated guesses for a(= K
h
/K
v
) values that range from 2 to
10 for natural aquifers (e.g. Kasenow 2010) results in poor
well design. The predicted additional head loss by partial pen-
etration is highly overestimated due to underestimating the in-
situ aquifer permeability at injection depth (Fig. 3b). In order
Fig. 2 Approximation of the hydraulic properties of the filter pack using
the modified Ergun relation (Van Lopik et al. 2017,2020b) obtained from
packed-bed flow experiments on filter sands and gravel (C
u
< 3) and
aquifer material (C
u
>3) for the ahydraulic conductivity and b
Forchheimer coefficient b
Hydrogeol J

to estimate the overestimation in head loss, this study consid-
ered a high-permeability layer (hydraulic conductivity of K
1
and thickness of H
1
) under- and overlain by low-permeability
layers (K
2
) of equal thickness (H
2
;Fig.3a). The average hor-
izontal hydraulic conductivity K
h,av
over the entire aquifer
thickness (Fig. 3b) is calculated by (Kasenow 2010):
Kh;av ¼∑Kh;iHi
Htot
ð16Þ
The average vertical hydraulic conductivity K
z,av
for both
the heterogeneous aquifer and the equivalent anisotropic ho-
mogeneous aquifer (see Fig. 3) is calculated by Kasenow
(2010):
Kz;av ¼Htot
∑Hi
Kz;i
ð17Þ
Results
Components of head loss in artificial recharge or
dewatering deep wells
The maximum recharge/discharge rate that is investigated for
the sandy aquifers (ACS-1 and AVCS-1) is 20 m
3
/h. This
results in very high total head losses in the range of 10.7–
15.7 m (Fig. 4a–b). At a rate of 10 m
3
/h, the total head losses
are in the range of 5.3–7.8 m, which are still high for well
operation in such sandy aquifers. No large differences in well-
efficiency between the naturally developed well-types
(WAC1–2) and well-types with filter pack (WFP1–2) are ob-
served (Fig. 4a–b). Comparing the analysis on the
components of head loss between the well-types WAC1–2
and WFP1–2, the difference in total head loss between the
two well completion methods is large for the wells screened
in coarse gravely aquifers (A-CG1–2; Fig. 4c–d). At recharge/
discharge rates of 20 m
3
/h in aquifer A-CG1, the total head
losses are only 2.45 and 2.16 m for WAC1 and WAC2 re-
spectively, while the total head losses for WFP1–2 are much
higher, with values of 6.35 and 5.39 m respectively (Fig. 4c).
For well completion with filter pack of well-types WFP1–2
with very coarse filter sand (FP-VCS1) in gravely aquifers A-
CG1–2, the head loss in the skin layer is the most important
contributor to the total head loss due to the assumption of a
low-permeability skin layer (K
sk
= 1E-6 m/s). At volumetric
recharge/discharge rates of 20 m
3
/h, the percentage of relative
head loss due to skin ranges between 65 and 80% of the total
head loss for well-types WFP1–2 that are screened in A-CG1–
2(Fig.4c–d). Hence, extensive well development after
reverse-circulation rotary drilling is required to remove filter
cake and increase the K
sk
to values of approximately 1E-3 m/s
in order to achieve similar head loss of 1.3 m, as for the
equivalent case with WAC2.
For the estimated additional head loss components in the
aquifer and collapsed aquifer zone for the naturally developed
well-types WAC1–2, a higher hydraulic conductivity (nega-
tive skin) for the collapsed aquifer is assumed (Fig. 1a). This
results in slightly reduced head losses in the collapsed aquifer
zone. For example, a volumetric recharge/discharge rate of 20
m
3
/h for WAC2 screened in the gravely aquifer ACG-1 results
in an estimated head loss of only 0.06 m in the collapsed
aquifer zone, which is only 4.3% of the total head loss (see
Fig. 4c). Compared to a scenario with no formation of nega-
tive skin layer and permeability enhancement after completion
and development of well-type WAC2 in the borehole area
(r
s
<r<r
b
), the estimated head loss is 0.21 m (Fig. 5c), which
is only 9.3% of the total head loss. Only for severe reduction
Fig. 3 Estimation of the additional well loss due to partial penetration, aassuming thewell isscreened in a high-permeability layer in the aquifer (K
1
)and
bassuming an equivalent anisotropic homogeneous aquifer
Hydrogeol J

of permeability (positive skin) in the borehole area (r
s
<r<
r
b
), the contribution to the total head loss can be significant.
For example, in order to obtain a similar total head loss as for
WFP1 at a discharge/recharge rate of 20 m
3
/h in A-CG1 (total
head loss of 6.35 m; Fig. 4c), the hydraulic conductivity in the
borehole area (r
s
<r<r
b
) needs to be reduced from 328 to
19 m/day (with bcoefficient of 23,700 s
2
/m
2
) for WAC2. This
can be the case for scenarios with poor or no well development
in the borehole area in WAC1–2.
Head losses in the filter pack and collapsed aquifer
zone
The selection of a proper very coarse filter sand (FP-VCS1
with K
fp
= 823 m/day) for well-types WFP1–2 results in lim-
ited additional head loss in the filter pack compared to head
losses in the skin layer and aquifer. The hydraulic conductivity
of the filter pack is a factor of 15.4 and 12.6 higher than the
aquifer hydraulic conductivities of A-CS1 and A-VCS1 re-
spectively. In contrast, the advantage of well completion with
filter pack FP-VCS1 (d
50
= 1.5 mm) in coarse gravel deposits
(A-CSG1–2) is limited, resulting in higher aquifer hydraulic
conductivities by a factor of only 2.5 and 1.6 respectively.
Therefore, the advantage of using filter packFP-VCS1 instead
of the actual aquifer material in the borehole area (r
s
<r<r
b
)
is small in the gravely aquifers (A-CG1–2). For example, the
difference in head loss at 20 m
3
/h with WFP1 between the
filter pack (Δh
fp
=0.075 m; Fig. 6d) and a hypothetical sce-
nario of aquifer material A-CG2 in the borehole area (Δh
aq
=
0.126 m; Fig. 5d) is negligible. For the sandy aquifers the
difference in head loss is much higher, where Δh
aq
equals
0.97 m (A-CS1) and 1.06 m (A-VCS1; Fig. 5a–b). The
Fig. 4 Head losses in the aquifer during artificial recharge/dewatering
with the four different well-types (Table 1) at volumetric discharge/
recharge rates (Q)overa1-mfilterlength(L)of5,10,20and30m
3
/h.
The aquifer types in Table 2are used with aA-CS1 (d
50
= 0.77 mm), bA-
VCS (d
50
=1.5mm),cA-CG1 (d
50
=9.5mm),dA-CG2 (d
50
= 6.3 mm).
Note that for well types WAC the collapsed aquifer hydraulic conductiv-
ity is two times higher than the aquifer material and for well types WFP
the filter pack F-VCS1 is considered
Hydrogeol J

selection of coarser, more permeable filter packs in homoge-
neous gravel aquifers could potentially increase the well effi-
ciency. The use of filter pack FP-VCS2 in a high-permeability
layer of A-CG2 could reduce the head loss significantly by a
factor of 2.7. However, the selection of coarser gravel packs
(d
50
> 2 mm) could resultin mobilization of fine material from
the well-graded gravel with fine sand/silt and the risk of sand
pumping (Powers et al. 2007). In practice, the selected grain
size of the uniformly graded filter packs by dewatering com-
panies for well completion in sandy natural aquifers are com-
monly 1.0–2.0 mm (e.g. FP-CS2 and FP-VCS1–2).
For wells screened in stratified aquifers, filter packs should
be based on the finest strata. As a consequence, the selection
of filter packs for well-types WFP1–2 based on the finer low-
permeability layers in highly heterogeneous sandy or gravely
aquifers does not necessarily mean significant reduction in
well losses compared to naturally developed well-types
without filter pack (WAC1–2). Most flow will occur in the
high-permeability layers in the aquifer such as A-CG1 (K=
328 m/day) and A-CG2 (K= 527 m/day). In such case, the use
of WFP1–2 for dewatering and artificial recharge does not
necessarily result in a better well performance than well-
types WAC1–2.
The nonlinear flow head losses in the filter packs are small
compared to the total head loss (Figs. 4and 6). Due to rela-
tively high Forchheimer coefficients bwith respect to the hy-
draulic conductivity of natural sands and gravels with high C
u
values and low porosity values compared to filter sands
(Table 2), the component of head loss due to nonlinear flow
behaviour is slightly higher for ACG1–2(Fig.5c–d).
Considering the use of well-types WAC1–2withnocollapsed
aquifer zone (negative skin) in these aquifer types, the per-
centage of nonlinear flow head loss is approximately still only
4% of the total head loss. Note that in typical collapsed aquifer
Fig. 5 Head losses in the borehole area of the aquifer during artificial
recharge/dewatering with the four different well-types (Table 1)atvolu-
metric discharge/recharge rates (Q) over a 1-m filter length (L)of10,20
and 30 m
3
/h. The head loss is calculated within the radius of the borehole
(r
s
<r<r
b
), to compare and investigate the efficiency increase with well
completion using a filter pack. The aquifer types in Table 2are used with
aA-CS1 (d
50
= 0.77 mm), bA-VCS (d
50
= 1.5 mm), cA-CG1 (d
50
=
9.5 mm), dA-CG2 (d
50
= 6.3 mm)
Hydrogeol J

zones (after well completion by jetting of straight-flush rota-
ry), the porosity is increased and the relative fraction of non-
linear flow behaviour head loss is lower. Therefore, one can
state that the effect of nonlinear flow behaviour on head loss is
limited for both naturally developed (WAC1–2) and filter
pack well-types (WFP1–2) in sandy to fine-gravelly aquifers
after proper well completion and development. This is in line
with the non-Darcian head losses in common water wells
(Barker and Herbert 1992;Houben2015a,b).
However, in uniformly graded gravely to boulder-type aqui-
fers, the effect of nonlinear flow behaviour will become more
significant. For example, considering a high-permeability aquifer
with the aquifer characteristics of FP-VCS2 (K= 1339 m/day)
and no well skin or filter pack on well-type WAC2, the total head
loss will be 0.84 m with a non-Darcian head loss component of
7% at Q=30m
3
/day. Therefore, screening well-types WAC1–2
in high-permeability gravel layers (K> 1,000 m/day), which will
allow for considerably higher volumetric discharge/recharge
rates, the additional head loss by nonlinear flow behaviour
should be taken into account.
SimilartoHouben(2015b), the additional head loss due to
flow convergence/divergence in the filter pack is negligible (e.g.
only <0.03% of the total head loss for WAC1–2andWFP1–2
with FP-VCS1; Figs. 4and 6d). The additional head losses due
to convergence/divergence are calculated based on the assump-
tion that the flow lines solely converge/diverge at the interface
between the filter pack and well screen, see Appendix. To deter-
mine if this is a proper assumption, numerical modelling and
Fig. 6 Head losses in the filter pack during artificial recharge/dewatering
with the four different well-types (Table 1) at volumetric discharge/
recharge rates (Q) over a 1-m filter length (L) of 10, 20 and 30 m
3
/h.
The considered types of filter packs (Table 2) are used with aFP-MS1 of
medium sand (d
50
= 0.39 mm), bFP-CS1 of coarse sand (d
50
=0.71mm),
cFP-CS2 of coarse sand (d
50
=1.0mm),dFP-VCS1 of very coarse sand
(d
50
= 1.5 mm) and eFP-VCS2ofverycoarsesand(d
50
= 2.1 mm). Note
that well-types WAC1–2 are usually completed without filter pack
Hydrogeol J

experimental work is required. Presumably, convergence or di-
vergence of flow lines during respectively abstraction or injec-
tion will not solely occur at this interface, but over a wider region
in the filter pack and is much more complex than the assumption
made in Appendix for Boulton’s equation (1947; Eq. 6).
Therefore, the components of head loss due to divergence or
convergence in the present study should be taken as a proxy.
Nonetheless, it makes sense that the major contribution of head
loss occurs by the axi-symmetric Darcian and nonlinear flow as
shown in Figs. 5and 6, and the zone of diverging/converging
flow lines occurs in the nearest vicinity of the screen, and will be
very small.
Clogging of the filter pack
Severe clogging of the filter pack of artificial recharge and
dewatering deep wells (well-type WFP1), could result in high
additional head losses (Fig. 7). For example, considering filter
pack FP-CS2, a porosity reduction to a value of 0.18 by clog-
ging could result in increased total head loss by a factor 2
during abstraction or recharge in aquifer A-VCS1. The reduc-
tion in well efficiency due to clogging by lower porosity
values is greatest for the filter pack with the lowest average
grain size (FP-MS1; d
50
= 0.39 mm). Assuming a reduction of
the porosity from a value of 0.34 to a value of 0.25, the addi-
tional head loss is increased by a factor of 7.5. This is only a
factor of 2.4 for the filter pack FP-VCS2 (d
50
= 2.0 mm). Note
that for naturally developed well types (with natural sands and
gravels with C
u
> 3 within the area r
s
<r<r
b
) the initial po-
rosities of the aquifer material can be significantly lower than
the porosities of uniformly graded filter sands. Hence, well-
types WAC1–2 with lower initial porosities of the aquifer
material in the vicinity of the well screen compared to equiv-
alent cases with filter pack might be more susceptible for
additional head loss due to well clogging over time.
Effect of partial penetration of wells
In general, optimal efficiency for water wells is obtained when
the filter screen is placed over a large portion of the aquifer in
order to reduce head losses by converging or diverging flow
lines in the vertical direction due to partial penetration (e.g.
Houben 2015a). However, in construction dewatering, PPWs
are used to target the desired hydraulic impact at a given depth
in the aquifer. Hence, the reduction in well efficiency on the
one hand, and the desired hydraulic impact at a given aquifer
depth on the other hand, need to be taken into account in order
to define the optimal well design. The optimal ratio of partial
penetration is a trade-off between these two issues.
The latter scenarios in the present study, assuming the
Dupuit-Forchheimer approximation with lateral flow behav-
iour in the entire aquifer system, can be considered as an upper
estimate of the maximum head loss of a PPW screened in a
given portion of the aquifer. In such scenario, all flow in the
screened portion of the aquifer (Q/L) is assumed to be in the
lateral direction, and no flow in the vertical direction towards
over- and underlying aquifer layers occurs.
In Fig. 8, the additional head loss due to partial penetration in
aquifer type A-VCS1 is shown using Eq. (14). Especially for
partial penetration ratios smaller than 0.2 the additional head loss
is significant, while considering an anisotropic, homogeneous
aquifer. Screening PPWs in the top or bottom of the aquifer (ε=
1inEq.15), the additional head loss due to partial penetration is
the highest. PPWs screened in the middle of the aquifer (ε=0in
Eq. 15) result in the smallest additional head loss for a given
partial penetration ratio (Fig. 8). These results are in line with the
numerical modelling results of Tügel et al. (2016), while con-
sidering uniform screen inflow at the abstraction PPW.
However, note that in practice, inflow and outflow over a
PPW screen is not constant over the entire filter length (e.g.
Ruud and Kabala 1997;Houben2015a; Tügel et al. 2016;
Fig. 7 Additional head loss in the
filter pack for well-type WFP1
(with FP-MS1, FP-CS2 and FP-
VCS2) due to porosity reduction
by clogging. The components of
head loss due to hydraulic con-
ductivity reduction (Fig. 2a)and
nonlinear flow increase (Fig. 2b)
are shown
Hydrogeol J

Zhu and Wen 2019).Thevolumetricflowrateatthetopand
bottom end of a PPW is generally higher than in the middle
portion of the well screen. Moreover, factors such as aquifer
heterogeneity (Ruud and Kabala 1997; Houben and Hauschild
2011), the pump position (Tügel et al. 2016) or nonlinear flow
behaviour in the well vicinity (Zhu and Wen 2019) could have
an impact on additional head loss calculations and require a
numerical approach and flow meter logs for more detailed in-
vestigation (e.g. Houben 2015b).
For heterogeneous aquifers, the assumption of equivalent
anisotropic homogenous aquifer conditions does not hold for
wells screened in a high-permeability layer while using low
partial penetration ratios (0.1 < p
p
< 0.5). The actual horizontal
hydraulic conductivity can be drastically underestimated by
using a simplified characterization of the aquifer with anisotrop-
ic homogeneous conditions. Table 4shows that poor aquifer
characterization by using one bulk K
h,av
and K
v,av
for the aniso-
tropic homogeneous aquifer results in drastic overestimation of
the additional head loss by partial penetration. Using a PPW of
well-type WFP-1 that screens a 2-m-thick high-permeability
layer of 328 m/day, under- and overlain by lower-
permeability layers of 32.8 m/day of 9-m thickness each, the
additional head loss by partial penetration is only 0.52 m
(Table 4). If the high-permeability layer is not taken into ac-
count and the simplified equivalent anisotropic homogenous
aquifer is considered, the additional head loss is overestimated
by a factor of 4 (2.0 m). Hence, the selection of the screen
interval depth of a dewatering deep well or artificial recharge
PPW should be based on good soil characterization in order to
minimize additional head loss by partial penetration.
Especially, the placement of an artificial recharge PPW to dis-
charge dewatered groundwater in a high-permeability layer
overlain by low-permeability strata could reduce the hydraulic
impact on the overlaying dewatered strata at a minimized addi-
tional head loss due to partial penetration.
Discussion
Differences in head loss due to well completion
method
The results in the present study suggest that use of relatively
cheap and quick drilling methods (jetting and straight flush
rotary) for well completion of well-types WAC1–2 without
placement of a filter pack does not necessarily mean increased
head losses and higher pumping costs. Especially, well screen
placement in high-permeability aquifers (A-CG1–2) with
WAC1–2 results in better well performance compared to
placement of WFP1–2 with reverse-circulation rotary drilling
(Fig. 4c–d). Comparing the well-types WAC1–2withnoclear
formation of a thin skin layer by filter cake and a zone of
collapsed aquifer (Fig. 1a) with wells drilled by reverse-
circulation rotary drilling with a positive skin layer (well-types
WFP1–2; Fig. 1b), the amount of total head loss by
discharging/recharging water at Qof 20 m
3
/h into or from
the gravely aquifers (A-CG1–2) is reduced by factors of 3–4.
Fig. 8 Additional head due to
partial penetration compared to an
equivalent scenario of a fully
penetrating well for well-type
WFP1 and a volumetric
discharge/recharge rate (Q)of10
m
3
/h in an aquifer of very coarse
sand (A-VCS1: d
50
=1.5mm).
The solid lines represent PPWs
screened in the centre of the
aquifer. The dashed lines repre-
sent PPWs screened at the top/
bottom of the aquifer (well screen
placed below/above confining
unit)
Hydrogeol J

Uncertainties in the hydraulic characteristics of the
well skin and collapsed aquifer zone
This study assumed a filter cake layer of 1 mm at r
b
(r
sk-in
<r
<r
sk-out
) with a hydraulic conductivity (K
sk
)of1e-6m/s.
Ideally, well development in formations of high hydraulic
conductivity should be applied for hours, and development
in formations of low hydraulic conductivity may take days
to remove the filter cake (Powers et al. 2007). However, in
practice, dewatering companies often choose to apply well
development over a limited time span for the smaller
dewatering projects that are operational over only a small
period of time. Especially compared to drinking-water, ASR
or ATES wells that are operational over a much longer time
span, the impact of skin layers on total head loss in dewatering
deep wells and artificial recharge wells can be large. As a
consequence, well completion with reverse-circulation rotary
drilling (e.g. WFP1–2) could result in a distinct skin layer.
Drilling with drilling mud, which is usually done with
reverse-circulation rotary drilling, will always result in a filter
cake and poorer well performance over time compared to
drilling techniques without drilling additives (Timmer et al.
2003). Hence, the assumption of a skin layer with K
sk
of 1e-
6 m/s for well-types WFP1–2 is a good indication for the
potential contribution of head losses due to skin in dewatering
and artificial recharge wells. In practice, the actual thickness
and hydraulic conductivity of the skin layer of such wells are
unknown, since no samples of the skin layer are available, and
these properties should be determined indirectly from
pumping tests (Barrash et al. 2006; Houben 2015a). So far,
only a few in-situ skin layer samples have been analyzed by
permeameter tests (e.g. Houben et al. 2016). Similar to the
latter study, in-situ sampling of the borehole area at well-
types such as WFP1–2 and WAC1–2 could provide useful
insight into the hydraulic characteristics of the skin layer and
filter pack on the one hand and the collapsed aquifer zone on
the other hand.
For well types WAC1–2, the assumption of an improved
collapsed aquifer zone (negative skin) with a hydraulic con-
ductivity reduction by a factor 2 is an optimistic estimate. In
reality, similar to the hydraulic conductivity of the skin per-
meability in the filter cake for WFP1–2, the permeability in
this collapsed aquifer zone could vary for each well depending
on aquifer type, well completion, and well development meth-
od. Using clean water as drilling fluid, the amount of fines in
this zone will be low and the assumption of enhanced perme-
ability is reasonable. However, poor well development or the
use of a bentonite mud or circulation water as drilling fluid
could cause permeability reduction in the collapsed aquifer
zone. Generally, dewatering companies in the Netherlands
are using clean surface water or groundwater to drill down
to depths of 20 m below ground level. Therefore, considering
no permeability reduction/enhancement in the collapsed zone
should provide a good estimate for the upper limit of head
losses in the initial stage of well operation for well-types
WAC1–2 after well completion and proper well development.
Only severe reduction of permeability in the collapsed
aquifer zone due to poor well development after well comple-
tion with jetting and straight-flush rotary drilling for WAC1–2
will result in high contributions to the total head loss in the
borehole area (r
s
<r<r
b
). Note that the absence of a filter
cake layer after aquifer collapse for WAC1 (Fig. 1a)allowsfor
easier, less extensive well development, which makes the as-
sumption of enhanced permeability or in-situ aquifer perme-
ability within the borehole area (r
s
<r<r
b
) reasonable.
Hence, the reduced total head loss in gravely aquifers by using
Table 4 Estimated additional head loss considering well-type WFP1 in a heterogeneous (Heterogen.) high-permeability layer and an equivalent case
with anisotropic homogeneous (Homogen.) aquifer conditions using Eq. (14)
Aquifer condition p
p
[−]K
1
[m/day] K
2
[m/day] B
1
[m] B
1
[m] Heterogen.
Δh
pp
[m]
(see Fig. 3a)
Anisotropic Homogen.
Δh
pp
[m]
(see Fig. 3b)
Aquifer A-VCS1 0.1 65.2 65.2 2 9 1.74 1.74
0.1 65.2 6.52 2 9 2.61 10.3
0.1 65.2 0.652 2 9 3.52 24.3
Aquifer A-VCS1 0.2 65.2 65.2 4 8 0.98 0.98
0.2 65.2 6.52 4 8 1.35 4.01
0.2 65.2 0.652 4 8 1.75 7.07
Aquifer A-CG1 0.1 328 328 2 9 0.35 0.35
0.1 328 32.8 2 9 0.52 2.04
0.1 328 3.28 2 9 0.70 4.82
Aquifer A-CG1 0.2 328 328 4 8 0.19 0.19
0.2 328 32.8 4 8 0.27 0.80
0.2 328 3.28 4 8 0.35 1.40
Hydrogeol J

WAC1–2 is a good indication of the potential advantage of
using WAC1–2 instead of WFP1–2.
Predicting additional head loss by well clogging
Well ageingof abstraction and recharge wells can occur due to
mechanical and geochemical clogging (De Zwart 2007;Van
Beek et al. 2009a,b;Houbenetal.2018). This proccess could
occur due to clogging of the filter pack, screen slots and well
casing interior (Houben et al. 2018). The most important con-
tributor to head loss by well ageing is clogging of the filter
pack, while increased head loss only occurs when there is
severe clogging of the screen slots and well casing interior.
In practice, clogging of the filter pack and screen slots can be
observed by the increasing difference in head over time be-
tween the abstraction water well itself and the observation
well in its gravel pack (Van Beek et al. 2009b). Moreover,
clogging could occur at the borehole interface between the
filter pack and aquifer material by the formation of a thin skin
layer (Timmer et al. 2003; De Zwart 2007; Van Beek et al.
2009b). Ongoing accumulation of fine materials at the bore-
hole wall causes this zone to slowly expand outwards and
increase in thickness, and hence increases flow resistance over
time during abstraction (higher Δh
sk
for Eq. 12).
During artificial recharge in a water well, the recharged
water always contains impurities that cause well clogging
(plugging) over time (Olsthoorn 1982; Bouwer 2002;Bear
2007; Powers et al. 2007; Martin 2013). These impurities
can range from organic matter, air entrainment, to fine aquifer
material (such as clay, loam or silt) or precipitates of minerals
(such as manganese- or iron-oxides and calcite). For recharge
wells, suspended solids or chemicals are transported into the
filter pack and aquifer. Moreover, rapid clogging of artificial
recharge wells immediately after the start of the recharge pro-
cedure could occur due to degassing of depressurized water
and formation of air bubbles in the filter pack or aquifer
(Olsthoorn 1982;Martin2013). Generally, clogging during
recharge occurs in the gravel pack (if present), the borehole
interface and in the target formation immediately surrounding
the borehole (Martin 2013).
The clogging of the filter pack or aquifer material, by par-
ticle migration, biofouling and mineral precipitation or free
gas, could result in significant porosity reduction. In the pres-
ent study, the clogging mechanism is determined by only re-
ducing porosity in the Ergun relationships (Eq. 3)basedon
packed bed experiments of filter sands at porosity values of
0.25–0.35. Exact determination of nonlinear flow behaviour
through severely clogged packed beds are required to investi-
gate to what extent nonlinear flow behaviour causes additional
head losses. This should be done for the various mechanisms
of clogging to obtain a more detailed overview of the extent to
which well clogging could cause additional head losses during
well operation. During well operation, there are methods to
analyze the clogging potential of an artificial well such as
membrane filtration index (MFI; for the suspended solid con-
tent of the recharged water) and assimilable organic carbon
content (AOC; for the growth potential of microorganisms in
water; Bouwer 2002).
Increasing injection pressure to maintain the desired recharge
rate of the well is not a successful solution to overcome the
problems of clogging. Such a solution could even lead to en-
hanced clogging potential, due to enhanced inflow of clogging
mass and compression of the clogging layer (Bouwer 2002).
Noncontinuous recharge schemes with periods of rest could
significantly enhance the well efficiency and reduce the effects
of clogging (Olsthoorn 1982; Bouwer 2002;DelaLoma
González 2013) by remobilization of finer particles by switching
from a rest period to recharge. A similar procedure is suggested
for groundwater abstraction (Van Beek et al. 2009a,b). Such
recharge schemes might be preferable for artificial recharge
wells near dewatering sites using a buffer container or two sets
of artificial recharge wells. Well development of artificial re-
charge and deep wells can be realized by a wide range of
methods such as brushing or scratching the inner screen surface,
surge (flushing) pumping, air lifting, or the use of chemicals
(Olsthoorn 1982;Powersetal.2007). In most cases, well devel-
opment could remove clogging particles from the well screen.
However, the development of the filter pack and aquifer is more
difficult, due to fractions of clogging particles that remain in the
filter pack, borehole wall or aquifer.
Conclusions
The present study provides a detailed overview of the contribu-
tions to the head loss for typical well configurations of dewatering
deep wells and artificial recharge wells. Typical well completion
methods in unconsolidated aquifers used by dewatering
companies are considered. To investigate the hydraulics of such
water wells, the method described by Houben (2015b) while using
the hydraulic characteristics of the filter pack and aquifer material
obtained from packed-bed flow experiments conducted by Van
Lopik et al. (2017 and 2020b)areused.
The well efficiency of wells drilled by relatively cheap and
quick drilling methods, such as jetting and straight-flush rota-
ry, without a proper well completion with a filter pack, does
not necessarily mean increased head losses and higher
pumping costs compared to wells completed with a filter pack
(with reverse-circulation rotary drilling). The main component
of head loss occurs in the aquifer for well completion without
filter pack by jetting or straight-flush rotary drilling. In such
case, the formation of negative skin in the borehole area and
no filter cake layer continuously spread over the entire bore-
hole wall can be considered due to aquifer collapse after re-
moving the drilling rod or jetting tube from the unconsolidated
soil. Only severe permeability reduction by residual mud
Hydrogeol J

additives or fines in the collapsed aquifer zone after poor well
development could result in positive skin for such wells. In
well-types with a filter pack (WFP), besides the component of
head loss in the aquifer itself, the contribution to the total head
loss by a positive skin layer of filter cake after well completion
can be significant. Especially for high-permeability aquifers,
the absence of a positive skin layer on the borehole wall in
wells completed without a filter pack results in equal or better
well performance compared to the more expensive drilling
method of reverse-circulation rotary drilling. Intensive and
costly well development would be required to lower the
amount of positive well skin on such wells to operate at sim-
ilar efficiency.
Selection of a proper filter pack (with average grain size of
1.0–2.0 mm) for wells screened in sandy to gravely aquifers
(50 < K< 500 m/day) results in only a minor contribution to
the total head loss. The component of head loss due to non-
linear flow behavior in the filter pack or aquifer is small, if
sandy to gravely aquifers (K< 500 m/day) and maximum dis-
charge or recharge rates of 30 m
3
/h over 1 m filter length are
assumed.
Clogging of the filter pack is considered by assuming uni-
form reduction of the porosity values. Due to the reduction of
the pore space, the main contributor to additional head loss by
filter pack clogging is the effect of nonlinear flow behavior.
Filter packs or aquifer material with smaller grain sizes and
low initial porosity values are more susceptible to increase in
head losses due to porosity reduction by clogging.
It is recommended that dewatering companies investi-
gate the characteristics of the aquifer prior to well installa-
tion of dewatering wells and artificial recharge wells.
Especially for PPWs, good aquifer characterization is re-
quired to screen artificial recharge wells in high-
permeability strata. Not accounting for heterogeneity in
aquifers with gravely strata could easily overestimate the
required well head by factors higher than 2 for PPWs with
small partial penetration ratios. Good exploration of the
dewatering site could promote the use of dewatering deep
wells and artificial recharge PPWs to minimize the hydrau-
lic impact of short-term dewatering operations. Moreover,
the selection of high-permeability layers could promote the
use of quick and cheap well completion without a filter
pack using jetting or straight-flush rotary drilling instead
of using full-penetration wells completed with filter pack
and extensive well development to remove the fines from
the filter cake layer.
Acknowledgements The authors wish to thank Georg J. Houben from
the Bundesanstalt für Geowissenschaften und Rohstoffe for his critical
comments on prior drafts of this paper and Dr. A. Mouraz Miranda and an
anonymous reviewer for their constructive feedback. Moreover, the au-
thors wish to thank dewatering companies Theo van Velzen, Henk van
Tongeren and P.J. de Vet & Zonen for providing well specifications of
typical dewatering deep wells and artificial recharge wells.
Funding This work was supported by the foundations STW (Foundation
for Technical Sciences) and O2DIT (Foundation for Research and
Development of Sustainable Infiltration Techniques).
Appendix
Solution for the Darcy-Forchheimer equation for
converging flow in filter packs towards screen slots
Inside a filter pack, groundwater flow is affected by the pres-
ence of well screens. During abstraction, groundwater has to
converge to the screen slots, which causes an additional head
called Δh
cv
.Boulton(1947) derived an equation for Δh
cv
based on the ratio (δ
s
)ofslotaperture(l) and circumference
of the well:
δs¼nsl
2πRð18Þ
where n
s
is the number of slots inside the circumference of a
well and Ris the radius of the well. The equation by Boulton
(1947) is given by (Houben 2015b):
Δhcv ¼Q
KfpLsns
ln 2
1−cosδsπ
 ð19Þ
where K
fp
is the hydraulic conductivity of the gravel pack and
L
s
is the length of the screen. Unfortunately, the derivation of
Boulton’s equation is not given in that article and therefore the
assumptions behind the equation are unknown; thus, a deriva-
tion of the equation for Δh
cv
is given in the following.
The starting point of the derivation is the Darcy-
Forchheimer equation, which is given by:
∂h
∂r¼−Q
2πrKfpLsns
−βQ
2πrKfpLsns

2
ð20Þ
where ris a radial coordinate. By separating variables, one can
obtain:
∂h¼−Q
2πKfpLsns

1
r∂r−βQ
2πKfpLsns

2
"#
1
r2∂rð21Þ
The Darcy-Forchheimer equation is independent of slot
aperture, therefore a geometric consideration is conducted be-
fore solving the Darcy-Forchheimer equation.
In order to obtain Boulton’s equation, the distance between
the well circumference and the opening (distance D) has to be
considered constant (see Fig. 9). This assumption implies that
flow remains radial inside the gravel pack until the groundwa-
ter is very close to the well. As a consequence, stagnant zones
of groundwater arise between the screen slots (see Fig. 9)
which forces the remaining groundwater towards the screen
Hydrogeol J

openings. Distance Dis defined for any circle having a radius
ras such that Dis constant (based on trigonometry; see
Fig. 9):
D¼R−H¼r1−cos θ
2

¼r1−cosπδðÞ ð22Þ
Differentiating Eq. (22), yields:
1
r∂r¼πsinπδ
1−cosπδ ∂δð23Þ
Using Eqs. (22 and 23), the Darcy-Forchheimer equation
becomes:
∂h¼−Q
2πKfpLsns

πsin πδðÞ
1−cos πδðÞ
∂δ

−β
D
Q
2πKfpLsns

2
"#
πsin πδðÞ∂δ
ð24Þ
In Eq. (24), the radial coordinates are projected on δcoor-
dinates, which represents flow perpendicular to the radius.
The boundary conditions for Eq. (24)are:
h¼hgp δ¼1
h¼hsδ¼δs
ð25Þ
Defining integration of Eq. (24)yields:
∫hgp
h¼hs
∂h¼−Q
2πKfpLsns

∫1
δ¼δs
πsin πδðÞ
1−cos πδðÞ
∂δ−β
D
Q
2πKfpLsns

2
"#
∫1
δ¼δsπsin πδðÞ∂δ
ð26Þ
Finally, one can obtain:
Δhcv ¼Q
2πnsKfpLs
ln 2
1−cosδsπ

−β
rs
Q
2πKfpLsns

2
ð27Þ
where the Forchheimer coefficient b¼β
K2
fp
References
Barker JA, Herbert R (1992) A simple theory for estimating well losses:
with application to test wells in Bangladesh. Appl Hydrogeol 0:20–
31
Barrash W, Clemo T, Fox JJ, Johnson TC (2006) Field, laboratory, and
modeling investigations of the skin effect at wells with slotted cas-
ing, Boise Hydrogeophysical Research Site. J Hydrol 326(1–2):
181–198
Basak P (1978) Analytical solutions for two-regime well flow problems. J
Hydrol 38(1–2):147–159
Bear J (ed) (1988) Dynamicsof fluids in porous media. Dover, New York
Bear J (ed) (2007) Hydraulics of groundwater. Dover, New York
Boulton NS (1947) Discussion of drawdown test to determine effective
radius of artesian well by C. E. Jacob. Trans Am Soc Civil Eng
112(1):1065–1068
Bouwer H (2002) Artificial recharge of groundwater: hydrogeology and
engineering. Hydrogeol J 10(1):121–142
Buscheck TA, Doughty C, Tsang CF (1983) Prediction and analysis of a
field experiment on a multilayered aquifer thermal energy storage
system with strong buoyancy flow. Water Resour Res 19(5):307–
1315
Cashman PM, Preene M (2013) Groundwater lowering in construction: a
practical guide to dewatering, 2nd edn. Taylor and Francis, Boca
Raton, FL
De Zwart AH (2007) Investigation of clogging processes in unconsoli-
dated aquifers near water supply wells. PhD Thesis, Technische
Universiteit,Delft,TheNetherlands
Driscoll FG (ed) (1986) Ground water and wells, 2nd edn. Johnson
Filtration Systems, St. Paul, MN
Engelund F (1953) On the laminar and turbulent flow of groundwater
through homogeneous sands. Transactions of the Danish Academy
of Technical Sciences, Copenhagen, A.T.S. 3, Bulletin 4, Hydraulic
Laboratories, Technical University of Denmark, Kongens Lyngby,
Denmark
Ergun S (1952) Fluid flow through packed columns. Chem Eng Prog
48(2):89–94
Fig. 9 Schematic overview of
flow convergence in the filter
pack (assumption by Boulton
1947)
Hydrogeol J

Forchheimer PH (1901) Wasserbewegung durch Boden [Movement of
water through soil]. Zeitschr Vereines Deutscher Ing 50(1736–
1741):1781–1788
Houben GJ (2015a) Review: Hydraulics of water wells—flow laws and
influence of geometry. Hydrogeol J 23(8):1633–1657
Houben GJ (2015b) Review: Hydraulics of water wells—head losses of
individual components. Hydrogeol J 23(8):1659–1675
Houben GJ, Hauschild S (2011) Numerical modeling of the near-field
hydraulics of water wells. Ground Water 49(4):570–575
Houben GJ, Halisch M, Kaufhold S, Weidner C, Sander J, Reich M
(2016) Analysis of wellbore skin samples: typology, composition,
and hydraulic properties. Ground Water 54(5):634–645
Houben GJ, Wachenhausen J, Guevara Morel CR (2018) Effects of age-
ing on the hydraulics of water wells and the influence of non-Darcy
flow. Hydrogeol J 26(4):1285–1294
Kasenow M (2010) Applied ground-water hydrology and well hydrau-
lics, 3rd edn. Water Resources Publ., Highlands Ranch, CO
de la Loma González B (2013) Clogging of deep well infiltration recharge
systems in the Netherlands. In: Martin R (ed) Clogging issues asso-
ciated with managed aquifer recharge methods. IAH Commission
on Managing Aquifer Recharge, Richmond North, VIC, Australia,
pp 163–173
Martin R (ed) (2013) Clogging issues associated with managed aquifer
recharge methods. IAH Commission on Managing Aquifer
Recharge, Richmond North, VIC, Australia
Moutsopoulos KN, Papaspyros INE, Tsihrintzis VA (2009) Experimental
investigation of inertial flow processes in porous media. J Hydrol
374(3–4):242–254
Olsthoorn TN (1982) Verstopping van persputten [The clogging of re-
charge wells]. Keuringsdienst voor Waterleidingartikelen KIWA
N.V, Rijswijk, The Netherlands
Powers P, Corwin A, Schmall P, Kaeck W (2007) Construction
dewatering and groundwater control, 3rd edn. Wiley, Hoboken, NJ
Pyne RDG (2005) Aquifer storage recovery: a guide to groundwater
recharge through wells, 2nd edn. ASR Systems, Gainesville, FL
Roscoe Moss Company (1990) Handbook of ground water development.
Wiley, New York
Ruud NC, Kabala ZJ (1997) Response of a partially penetrating well in a
heterogeneous aquifer: integrated well-face flux vs. uniform well
face flux boundary conditions. J Hydrol 194:76–94
Timmer H, Verdel J-D, Jongmans AG (2003) Well clogging by particles
in Dutch well fields. J Am Water Works Ass 95(8):112–118
Tügel F, Houben GJ, Graf T (2016) How appropriate is the Thiem equa-
tion for describing groundwater flow to actual wells? Hydrogeol J
24(8):2093–2101. https://doi.org/10.1007/s10040-016-1457-0
Van Beek CGEM, Breedveld RJM, Juhász-Holterman M, Oosterhof A,
Stuyfzand PJ (2009a) Cause and prevention of well bore clogging
by particles. Hydrogeol J 17(8):1877–1886
Van Beek CGEM, Breedveld RJM, Stuyfzand PJ (2009b) Preventing two
types of well clogging. J Am Water Works Assoc 101(4):125–134
Van Lopik JH (2020) Design of recharge and abstraction well systems in
heterogeneous aquifers: modeling and experimental studies. In: PhD
Thesis, Utrecht University, Utrecht, The Netherlands
Van Lopik JH, Snoeijers R, van Dooren TCGW, Raoof A, Schotting RJ
(2017) The effect of grain size distribution on nonlinear flow behav-
ior in sandy porous media. Transp Porous Med 120(1):37–66
Van Lopik JH, Hartog N, Schotting RJ (2020a) Taking advantage of
aquifer heterogeneity in designing construction dewatering systems
with partially penetrating recharge wells. Hydrogeol J. https://doi.
org/10.1007/s10040-020-02226-7
Van Lopik JH, Zazai L, Hartog N, Schotting RJ (2020b) Nonlinear flow
behavior in packed beds of natural and variably graded granular
material. Transp Porous Med 131:957–983
Zhu Q, Wen Z (2019) Combined role of leaky and non-Darcian effects on
the flow to a pumping well with a non-uniform flux well-face
boundary. J Hydrol 580:123532. https://doi.org/10.1016/j.jhydrol.
2019.02.058
Zuurbier KG, Zaadnoordijk WJ, Stuyfzand PJ (2014) How multiple par-
tially penetrating wells improve the freshwater recovery of coastal
aquifer storage and recovery (ASR) systems: a field and modeling
study. J Hydrol 509:430–441
Hydrogeol J