Hydrol. Earth Syst. Sci., 18, 227–241, 2014
www.hydrol-earth-syst-sci.net/18/227/2014/
doi:10.5194/hess-18-227-2014
© Author(s) 2014. CC Attribution 3.0 License.
Hydrology and 
Earth System
Sciences
O
pen A
ccess
Representation of water abstraction from a karst conduit with
numerical discrete-continuum models
T. Reimann1, M. Giese2, T. Geyer2, R. Liedl1, J. C. Maréchal3, and W. B. Shoemaker4
1Institute for Groundwater Management, TU Dresden, Dresden, Germany
2Geoscientific Centre, University of Göttingen, Göttingen, Germany
3Bureau de Recherches Géologiques et Minières (B.R.G.M.), Montpellier, France
48307 Balgowan Road, Miami Lakes, FL 33016, USA
Correspondence to: T. Reimann (thomas.reimann@tu-dresden.de)
Received: 20 February 2013 – Published in Hydrol. Earth Syst. Sci. Discuss.: 8 April 2013
Revised: 15 November 2013 – Accepted: 23 November 2013 – Published: 17 January 2014
Abstract. Karst aquifers are characterized by highly con-
ductive conduit flow paths embedded in a less conductive
fissured and fractured matrix, resulting in strong permeabil-
ity contrasts with structured heterogeneity and anisotropy.
Groundwater storage occurs predominantly in the fis-
sured matrix. Hence, most mathematical karst models as-
sume quasi-steady-state flow in conduits neglecting conduit-
associated drainable storage (CADS). The concept of CADS
considers storage volumes, where karst water is not part of
the active flow system but hydraulically connected to con-
duits (for example karstic voids and large fractures). The
disregard of conduit storage can be inappropriate when di-
rect water abstraction from karst conduits occurs, e.g., large-
scale pumping. In such cases, CADS may be relevant. Fur-
thermore, the typical fixed-head boundary condition at the
karst outlet can be inadequate for water abstraction scenarios
because unhampered water inflow is possible.
The objective of this work is to analyze the significance
of CADS and flow-limited boundary conditions on the hy-
draulic behavior of karst aquifers in water abstraction sce-
narios. To this end, the numerical discrete-continuum model
MODFLOW-2005 Conduit Flow Process Mode 1 (CFPM1)
is enhanced to account for CADS. Additionally, a fixed-head
limited-flow (FHLQ) boundary condition is added that lim-
its inflow from constant head boundaries to a user-defined
threshold. The effects and the proper functioning of these
modifications are demonstrated by simplified model stud-
ies. Both enhancements, CADS and FHLQ boundary, are
shown to be useful for water abstraction scenarios within
karst aquifers. An idealized representation of a large-scale
pumping test in a karst conduit is used to demonstrate that
the enhanced CFPM1 is able to adequately represent water
abstraction processes in both the conduits and the matrix of
real karst systems, as illustrated by its application to the Cent
Fonts karst system.
1 Introduction
Karst aquifers can be described as triple porosity systems
with continuous primary porosity in the matrix, secondary
porosity within fissures and fractures, and tertiary porosity
represented by solution-enlarged features, i.e., highly perme-
able conduits (Worthington et al., 2000). Different concep-
tual approaches regarding karst aquifer storage are presented
in literature (Bakalowicz, 2005). Mangin (1975, 1994) at-
tributed large water storage to poorly interconnected large
voids adjacent to conduit systems, which transmit water
from the groundwater table towards a spring (annex sys-
tems to drainage). Mangin (1994) further assumes that ma-
trix storage is negligible. In contrast, Drogue (1974, 1992)
proposed areal water storage in the hydraulically continu-
ous matrix drained by the highly permeable karst conduit
system. Storage directly associated with discrete conduits
was not considered. However, the existence of water stor-
age within highly permeable karst structures is known from
karst hydraulics (e.g., Cornaton and Perrochet, 2002; Geyer
et al., 2008; Maréchal et al., 2008). Worthington et al. (2000)
and Worthington (2007) presented field studies that clearly
emphasize the necessity to describe karst aquifers as triple
porosity systems.
Published by Copernicus Publications on behalf of the European Geosciences Union.
228 T. Reimann et al.: Representation of water abstraction
Strong permeability contrasts within triple porosity sys-
tems lead to uncertainties during characterization of these
systems with conventional experimental, analytical, and nu-
merical methods (Geyer et al., 2013). For example, artificial
tracer tests are suitable methods for characterization of large
karst conduit systems (e.g., Atkinson et al., 1973). However,
tracer methods fail to characterize matrix properties on a
catchment scale. In contrast, conventional hydraulic borehole
tests provide useful information about local aquifer proper-
ties but also are unable to determine hydraulic information
on catchment scale because of limited pumping rates.
Only a few experiments are documented that address an
integral large-scale characterization of karst aquifers. In par-
ticular, Maréchal et al. (2008) performed a pumping test
with abstraction rates up to several hundred liters per sec-
ond for about one month. These high abstraction rates were
possible because the pumping well was directly connected
to the conduit system. The pumping test produced draw-
downs in both the conduit system and the fissured matrix
and, therefore, provided evidence to infer the existence of
large water storages within the fissured matrix and the con-
duits (Maréchal et al., 2008), see Fig. 1. Amongst others, di-
agnostic plots of drawdown and the logarithmic derivative of
the drawdown over time on a log-log plot (Bourdet et al.,
1983) were used to interpret the pumping test drawdown. At
early times, the drawdown and the derivative follow a straight
line of unit slope indicating the dominance of storage effects
(e.g., Bourdet et al., 1983; Renard et al., 2009), i.e., wellbore
storage, or interchangeable for directly pumping from karst
conduits, karst conduit storage. This unit slope of drawdown
and derivative is present during about the first 1000 min of
the large-scale pumping test, i.e., for early times (Fig. 6 in
Maréchal et al., 2008).
Further evaluation of large-scale field experiments for
karst characterization can be achieved by numerical mod-
eling, ideally with an approach that considers both ma-
trix and conduits with distributed parameter fields. Lumped-
parameter modeling approaches for simulation of karst hy-
draulics do not consider a distributed hydraulic parameter
field, e.g., Geyer et al. (2008), Maréchal et al. (2008) and
others. Halihan and Wicks (1998) introduced a model ap-
proach of pipes with smoothly turbulent flow that connect
reservoirs to represent conduit-flow aquifers, i.e., flow into or
out of the matrix is not considered. This idea to align reser-
voirs and flow restrictions in series was applied by Prelovšek
et al. (2008) to karst systems in Slovenia. Covington et
al. (2009) presented physically more enhanced representa-
tions of single karst network elements like full pipes, open
channels and reservoirs. However, a primary limitation of
this model is that it is only applied to single karst network
elements without the consideration of matrix interaction.
Discrete-continuum (or “hybrid”) models, which couple a
discrete pipe flow model to a continuum model, represent
a suitable approach to simulate karst aquifers (e.g., Király,
1998, 2002; Sauter et al., 2006; Kaufmann, 2009) without
neglecting the matrix interaction and under consideration
of strongly anisotropic hydraulic parameter fields. Liedl et
al. (2003) presented a discrete-continuum model for the sim-
ulation of laminar and turbulent pipe flow coupled to a con-
tinuum that represents the matrix. This approach was further
developed as Conduit Flow Process Mode 1 (CFPM1) for
MODFLOW-2005 (Shoemaker et al., 2008). This discrete-
continuum model approach was applied in a number of mod-
eling studies presented in scientific literature (e.g., Liedl
et al., 2003; Bauer et al., 2003; Birk et al., 2006; Hill et
al., 2010). However, discrete-continuum models based on
the Liedl et al. (2003) approach simulate conduit flow as
quasi-steady without drainable storage. Consequently, these
discrete-continuum models fail to simulate transient water
storage within the conduit system because steady-state pipe
flow equations are applied, i.e., drainable conduit storage is
not considered. For this reason, transient water storage can
be considered by the continuum model only. Following this,
Reimann et al. (2011) presented a discrete-continuum model-
ing approach to simulate unsteady discrete flow in a variably
filled pipe network employing the Saint-Venant equations,
while de Rooij (2008) and de Rooij et al. (2013) additionally
considered surface flow and variably saturated matrix flow.
The approach appears to be suitable for fundamental studies
but high parameter demand and computational effort can be
identified as potential drawbacks.
The objective of this work is to provide a distributive
process-based modeling approach based on the Liedl et
al. (2003) approach that allows the simulation of hydraulic
impacts (water abstraction, large-scale hydraulic tests, dis-
charge events) on karst systems with manageable data de-
mand and computational effort, under consideration of im-
portant storage processes. For that reason, the discrete-
continuum modeling approach of CFPM1 was further en-
hanced by adding water storage in parallel to the conduits.
In the following, we refer to this as conduit-associated drain-
able storage (CADS). Scenarios with direct water abstrac-
tion from the conduits can result in a reversion of the flow
direction, i.e., inflow at the karst spring (e.g., Maréchal et
al., 2008). Hence, the numerical model was complemented
by a constrained boundary condition according to Bauer et
al. (2005) to avoid unhampered water inflow through the
spring. The performance of the numerical model is evaluated
by a verification test and highly simplified synthetic scenar-
ios. Subsequently, an idealized model representation of the
large-scale pumping test at the Cent Fonts karst system" be-
hind large-scale pumping test (Maréchal et al., 2008) is con-
sidered as application outlook to demonstrate the potential
and benefits of the enhanced discrete-continuum model un-
der field conditions.
Hydrol. Earth Syst. Sci., 18, 227–241, 2014 www.hydrol-earth-syst-sci.net/18/227/2014/
T. Reimann et al.: Representation of water abstraction 229
Fig. 1. Left: schematic sketch of the Cent Fonts catchment, where a large-scale and long-term pumping test was conducted (Maréchal et al.,
2008); right: abstraction rate and drawdown in both matrix and conduit for a long-term and large-scale pumping test; figures from Maréchal
et al. (2008).
Fig. 2. Left: Sketch of a karst aquifer with (A) porous rock matrix,
(B) small fissures/fractures, (C) solution-enlarged conduits with ac-
tive flow, (SF1) solution-enlarged fractures, and (SF2) other karst
cavities, both without active flow. Right: discrete-continuum model
concept with (1) matrix continuum, (2) discrete pipes, and conduit-
associated drainable storage (CADS).
2 Modeling approach
This section introduces the concept of conduit-associated
drainable storage and implementation of this concept
within the numerical discrete-continuum model CFPM1
(Shoemaker et al., 2008). Further explanation is given about
the implementation of a flow constrained boundary condition
in CFPM1.
2.1 Conceptual consideration of conduit-associated
drainable storage
In general, storage in karst systems occurs in (A) the porous
matrix (primary porosity), (B) fractures/fissures (secondary
porosity), and (C) solution-enlarged pathways like conduits
(tertiary porosity), Fig. 2 left. The discrete-continuum model
concept considers two compartments: (1) a representative el-
ementary volume (REV) of the fissured/fractured matrix sim-
ulated as continuum with laminar flow and storage (matrix
continuum), and (2) solution-enlarged highly permeable con-
duits simulated as discrete pipe network with laminar and
turbulent flow without storage (active flow system). Existing
discrete-continuum models with steady pipe flow equations
provide drainable storage only by the matrix continuum.
Dynamic processes like water abstraction, however,
demonstrate that additional fast-responding local storage is
present (e.g., Maréchal et al., 2008). This fast responding
storage is assumed to be provided by features like solution-
enlarged fractures (SF1), and other cavities (SF2) that are
directly associated (connected) to the conduit flow system
but do not actively participate in pipe flow, i.e., conduit-
associated drainable storage. Figure 2 illustrates this concept.
2.2 Technical implementation into MODFLOW-2005
Conduit Flow Process (CFP)
2.2.1 Numerical discrete-continuum model CFP
Mode 1
Shoemaker et al. (2008) incorporated the discrete-continuum
model approach of Liedl et al. (2003) in MODFLOW-2005
as CFPM1. Laminar groundwater flow in the continuum
model is represented by the Darcy equation:
∂
∂x
(Kxx
∂hm
∂x
)+ ∂
∂y
(Kyy
∂hm
∂y
)+ ∂
∂z
(Kzz
∂hm
∂z
)±W
= Ss(∂hm
∂t
), (1)
with K hydraulic conductivity along the x, y, and z axes
(LT−1], hm matrix head [L], W volumetric flux per unit vol-
ume [T−1], Ss specific storage [L−1] and t time [T] (McDon-
ald and Harbaugh, 1988). Further details regarding the solu-
tion of the groundwater flow equation are well documented
in MODFLOW manuals and, therefore, not included here.
The conduit system is represented by nodes that are con-
nected by cylindrical pipes. Detailed explanation about the
discrete pipe model is given by Shoemaker et al. (2008). Fol-
lowing, a short overview is provided. Volume conservation
at each node is expressed by Kirchhoff’s law (Horlacher and
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230 T. Reimann et al.: Representation of water abstraction
Fig. 3. Conceptual drawing of CADS consideration in CFPM1.
Lüdecke, 1992):
0 =
np∑
i=1
Qip −Qss , (2)
where Qip is discharge from pipe i (up to n pipes) [L3T−1]
and Qss is the sum of flow from sinks and sources [L3T−1].
Laminar pipe flow is represented by the Hagen–Poiseuille
equation:
Qip =−
pid4ipg1hc,ip
128ν1lip
, (3)
with dip diameter of pipe i [L], g gravitational accelera-
tion [LT−2], 1hc,ip head difference along pipe i, ν kine-
matic viscosity of water [L2T−1], and lip length of pipe i [L]
(Shoemaker et al., 2008). Turbulent pipe flow is considered
by the Darcy–Weisbach equation with the friction factor ac-
cording to the Colebrook–White equation (Shoemaker et al.,
2008):
Qip =−
√√√√ |1hc,ip|gd5ippi2
21lip
log
 2.51ν√ 2|1hc,ip|gd3ip
1lip
+ kc,ip
3.71dip

1hc,ip
|1hc,ip| , (4)
with kc,ip mean roughness height of pipe i [L]. The cou-
pling between pipe network and continuum model is realized
through a head-dependent exchange flow rate Qex:
Qex = αex(hc −hm), (5)
where hc [L] is the conduit head, hm [L] is the matrix head,
and αex [L2T−1] is the pipe conductance (Barenblatt, 1960;
Shoemaker et al., 2008). Water transfer Qex between matrix
and conduits is considered for each node by MODFLOW as
external flow and by the pipe system as sink or source (term
Qss in Eq. 2).
2.2.2 Implementation of CADS
To consider drainable conduit storage within CFPM1, the
CADS package was developed. Conceptually, CAD storage
is assumed to be in direct hydraulic contact with draining
conduits, see Fig. 3, so that
hCADS = hc , (6)
where hCADS is the head [L] in the CAD storage. The CAD
storage is conceptualized as a rectangular block directly as-
sociated with the pipe, i.e., the CADS base area is the pipe
length associated with a node times the width of the CAD
storage (Fig. 3). Finally, the volume of the CADS for each
node is computed as
VCADS = lCADSWCADS(hCADS − zbot);hCADS > zbot , (7)
where lCADS is the length [L] (=∑ length of pipes associ-
ated to a node), WCADS is the width of the CAD storage [L],
and zbot is the elevation of the pipe bottom [L]. The ratio
VCADS/(hCADS – zbot) corresponds to the free-surface area
of the dewatering conduit network defined by Maréchal et
al. (2008). It is assumed that water released from the CADS
due to head variations immediately enters the pipe resulting
in additional discharge. The resulting discharge from CADS
storage, QCADS [L3T−1], is considered as
QCADS = Vt −Vt−1t
1t
, (8)
where Vt is the volume of the CAD storage [L3] at the time
t and 1t is the time step size [T]. QCADS is directly added
to the CFPM1 system of equations (represented by Qss in
Eq. 2) and subsequently considered for the iterative solution.
2.2.3 Implementation of a constrained fixed-head
boundary condition
A conduit with a fixed-head boundary condition can strongly
affect in- or outflow of the highly permeable pipe network
at the outlet, i.e., a karst spring. For example, water abstrac-
tion from a distinctive and well developed pipe network can
result in unlimited water inflow through a fixed-head bound-
ary. However, this contradicts the drawdown behavior in field
situations (e.g., Maréchal et al., 2008; Fig. 1). The fixed-head
limited-flow (FHLQ) boundary condition is intended to limit
inflow for constant head boundaries. If a user-defined dis-
charge threshold is exceeded, the fixed-head boundary con-
dition switches to a fixed-flow boundary condition, which re-
sults in a variable head (Bauer et al., 2005):
FHLQ=
{
hc = H, Q≤QL
Q = QL, else (9)
with H fixed head value (FH) [L], Q discharge at the bound-
ary (negative values denote outflow) [L3T−1], and QL limit-
ing discharge (LQ) [L3T−1]. H and QL are to be defined by
the user according to site-specific conditions.
3 Test scenarios
The functionality of conduit-associated drainable storage in
CFPM1 is verified by draining an isolated conduit with
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T. Reimann et al.: Representation of water abstraction 231
Fig. 4. Drainage behavior of CAD storage associated with an iso-
lated conduit to verify the CADS implementation in CFPM1.
CADS. Subsequently, a highly simplified model is used to
test the interaction of a conduit with CADS and the matrix
continuum for water abstraction setups under specific bound-
ary conditions.
3.1 Verification test with an isolated conduit
The test setup considers an lp = 500 m-long pipe that is sub-
divided by 6 nodes and 5 equally long tubes with a ra-
dius of r = 0.05 m and a bottom elevation of 0 m. CAD
storage is considered for the upstream node only (node 1)
with WCADS = 0.1 m and a node-associated conduit length
of lCADS = 50 m. An initial inflow of Q0 = 1.0 m3 s−1 is
applied to node 1 and a fixed head of 50 m is considered
as downstream boundary condition at node 6. Inflow stops
immediately at t = 0 and, subsequently, CAD storage is
drained. The resulting (drainage) flow Qd can be described
by the recession function from Maillet (1905).
Qd =Q0e−βt (10)
with
β = pir2 Kc
WCADSlCADSlp
, (11)
with Kc hydraulic conductivity of the conduit [LT−1]. Con-
duit flow is assumed as laminar with Kc = 2340 ms−1 ac-
cording to the Hagen–Poiseuille equation (e.g., Shoemaker
et al., 2008, p. 8). The resulting upstream head in node 1 is
77.163 m, respectively 1h is 27.163 m.
The recession discharge along time, computed by Eq. (10)
and by CFPM1 with CADS, is presented in Fig. 4. Both
results are equal and, therefore, demonstrate the ability of
CADS to represent the dynamic behavior of storage that
is directly coupled with a conduit. After drainage is com-
pleted, i.e., conduit heads are equal to the fixed head of
50 m, CFP budget files account for 135.814 m3 of water
released from CADS. This equals WCADS × lCADS ×1h
= 0.1 m× 50 m× 27.163 m and, therefore, verifies the
implementation of CADS in CFPM1.
Fig. 5. Sketch of the model setup used for testing the CADS and
FHLQ functionality.
3.2 Simple coupled system
In this section, the interactions of pipes with CADS with a
matrix continuum under different boundary conditions are
investigated. The intention of the test examples is to demon-
strate the functioning of the model enhancements in a sim-
plified (and therefore traceable) environment to allow a sys-
tematic process study.
3.2.1 Basic model setup
The basic model setup consists of a continuum model with
11 columns and 11 rows where each cell is 100 m× 100 m
(Fig. 5). Hydraulic conductivity and storage coefficient of
the matrix continuum are set as Km = 1× 10−5 ms−1 and
Sm = 0.01, respectively. The embedded conduit consists of
6 nodes connected by 5 tubes (each 100 m long). The pipe
diameter for one model realization is 0.5 m and for another
model realization 2.5 m. Pipe roughness height kc is set to
0.01 m. Water transfer between conduits and matrix is param-
eterized by a fixed water transfer coefficient per unit length
αex/lp = 1× 10−5 ms−1. All lateral outer boundaries of the
matrix continuum are of Neumann type (no flow). Diffuse
areal recharge is uniformly applied to the continuum with
8.26× 10−8 ms−1 and direct point recharge of 0.1 m3 s−1 is
applied to conduit node 1 (Fig. 4). The karst spring is rep-
resented by a fixed head of 50 m at conduit node 6. Water
abstraction occurs in node 5. The model simulates three pe-
riods, specifically: (1) pre-pumping from 0 to 86 400 s (1 day
duration); (2) pumping from 86 400 to 345 600 s (3 days du-
ration) at rates of 0.3, 0.5, and 1.0 m3 s−1, respectively, and
(3) recovery from 345 600 to 604 800 s (3 days duration).
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232 T. Reimann et al.: Representation of water abstraction
Fig. 6. Simulation results for the basic model (without CADS): conduit head at the pumping well, flow at the conduit constant-head boundary
condition (here multiplied by 0.1) and matrix transfer for different pumping rates of 0.3, 0.5, and 1.0 m3 s−1 respectively; left: conduit
diameter= 0.5 m; right: conduit diameter = 2.5 m (note that the scales for conduit heads differ in both figures).
3.2.2 Results for the basic model (available CFPM1
without CADS)
The resulting conduit heads, flow from matrix transfer and
flow at the fixed head (node 6) along time are shown in Fig. 6.
For stress period 1, spring discharge equaled 0.2 m3 s−1 (de-
noted as negative flow at the fixed head) and consisted of
diffuse areal recharge (0.1 m3 s−1) that enters the conduit as
matrix transfer flow plus direct point recharge to the con-
duit (0.1 m3 s−1 at node 1, see Fig. 5). Water abstraction in
period 2 from node 5 results in an immediate conduit head
drawdown to quasi-steady conduit heads and an immediate
variation of fixed-head flow (spring discharge) in order to
balance the water deficit. The resulting pipe flow influences
the head gradient of the pipes and, consequently, influences
water transfer from the matrix (see Eq. 5) that, in turn, af-
fects matrix heads. The efficiency of this process increases
with decreasing hydraulic capacity of pipes (smaller diame-
ter and/or larger roughness) and increasing pipe flows. For
the investigated setup, only the conduit diameter of 0.5 m
was found to be hydraulically limiting resulting in noticeable
head loss along the conduit and, therefore, clearly marked
drawdown at the pumping well (Fig. 6). However, the in-
creased water transfer between matrix and conduit induced
by conduit drawdown is much smaller than the inflow from
the fixed head. Water abstraction from the pipe with 2.5 m
diameter does not result in notable conduit drawdown be-
cause conduit hydraulics are not limiting. Consequently, wa-
ter transfer between matrix and pipes is not affected by water
abstraction and basically unhampered water inflow through
the fixed-head boundary occurs (Fig. 6).
After water abstraction is stopped in period 3, conduit
heads immediately rise up to pre-pumping values (Fig. 6). If
matrix heads were decreased by preceding water abstraction,
i.e., increased water transfer due to conduit head drawdown,
actual water transfer will react and matrix heads will return
to initial values. This process is reflected by a characteristic
delayed rerise of matrix transfer (see Fig. 6 left for the 0.5 m
diameter conduit and an abstraction rate of 1.0 m3 s−1).
In summary, this model setup highlights the necessity of a
constraining boundary condition for the karst spring to simu-
late karst water abstraction from conduits. Further, the imme-
diate reaction of conduit drawdown to the onset of water ab-
straction indicates the necessity of fast storage consideration.
3.2.3 Model enhancement with CADS and the FHLQ
boundary condition
The basic model setup (previous section) results in immedi-
ate drawdown due to water abstraction because steady-state
pipe flow equations do not consider conduit storage. For
that reason, the initial model is enhanced by adding CAD
storage. The CADS width WCADS is set to 0.25, 0.50, and
1.00 m, respectively, for three different model realizations.
An additional model run with WCADS = 0.00 m is performed
for comparison. As previously discussed, the basic model
setup demonstrated that in cases of unlimited conduit hy-
draulics water inflow through the fixed-head boundary domi-
nates (Fig. 6). The fixed-head limited-flow (FHLQ) bound-
ary condition can constrain inflow through the fixed-head
boundary resulting in limited inflow to the conduit system.
Subsequently, water abstraction of 0.30 m3 s−1 (node 5) is
considered and the fixed-head boundary condition of the ba-
sic model setup was extended by a flow constraint (LQ) of
0.025 m3 s−1 water inflow (node 6, compare Fig. 3). Conse-
quently, the water deficit of 0.10 m3 s−1 (0.20 m3 s−1 direct
and diffuse recharge minus 0.30 m3 s−1 water abstraction) is
balanced by spring inflow not exceeding 0.025 m3 s−1 (25 %
of the deficit) and additional flow from the matrix contin-
uum via water transfer and from the CAD storage of, in to-
tal, 0.075 m3 s−1 (75 % of the deficit). Model runs were per-
formed with conduit diameters equal to 0.5 and 2.5 m result-
ing in a similar behavior. Hence, only findings for the d =
0.5 m conduit are presented in detail. Contrary to the basic
setup without CADS and FHLQ, significant conduit and ma-
trix head drawdown is expected. Hence, log-log diagnostic
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T. Reimann et al.: Representation of water abstraction 233
plots of conduit drawdown, s, and drawdown derivative, s ′ ,
are depicted. The drawdown derivative is computed as (fur-
ther details in Bourdet, 1989)
s
′ = ∂s
∂ ln t
. (12)
Results are presented in Fig. 7. A water deficit occurs
with onset of water abstraction (period 2, day 2). Subse-
quently, the initially fixed-head boundary condition (node
6) switches to limited flow where inflow is restricted to
0.025 m3 s−1 (Fig. 7a). Without CADS, the model balances
the water deficit by instantaneously increased matrix trans-
fer that originates by an instantaneous drop of conduit heads
(Fig. 7a, b, see also Eq. 5). If CAD storage is consid-
ered, the water deficit is balanced by matrix transfer and
CADS flow whereas CADS flow decreases with ongoing
time, matrix transfer increases with ongoing time and CADS
flow dominates early times (Fig. 7b). Accordingly, conduit
heads change less abruptly than without CADS. This effect
is increased with increasing CADS width, i.e., more CADS
results in less matrix transfer and more damped conduit head
drawdown along time. Finally, after a quasi-steady state is
reached, matrix transfer is similar to model runs without
CADS (Fig. 7a, b).
The log-log diagnostic plots (Fig. 7c) clearly indicate the
impact of CADS, which acts as karst conduit storage (sim-
ilar to well bore storage). The presence of this fast storage,
indicated by the unit slope of conduit drawdown and draw-
down derivative, is increased with increasing CADS (pa-
rameterized through WCADS, Fig. 7c). The model without
CADS does not show any karst conduit storage in the log-
log diagnostic plot.
Water transfer between matrix and conduits affects matrix
heads. Consequently, matrix head drawdown is induced by
karst water abstraction from conduits. The more water trans-
fer the more matrix drawdown occurs (Fig. 7d), whereas the
absolute matrix drawdown is also dependent on matrix pa-
rameters (conductivity and storage). It may be noted that ini-
tial matrix heads do not depend on WCADS as this parame-
ter does not affect initial conduit heads but only alters the
amount of water stored in the CADS. During pumping, how-
ever, drawdown in the matrix is slowed down for increased
WCADS because more water is abstracted from the CADS in
this case.
Subsequently, after water abstraction is stopped (period 3,
day 5), the model without CADS does not consider any water
deficit. Consequently, the limited-flow boundary at the out-
let node 6 switches back to a fixed head and conduit heads
recover immediately to pre-pumping values. Because matrix
heads are still depressed (Fig. 7d), water transfer from the
matrix to the conduits needs some time to recover to the ini-
tial value (Fig. 7b, Eq. 5), and spring flow (negative fixed-
head flow at node 6) accordingly returns to initial values
(Fig. 7a, b). If CADS is considered, the water deficit is still
existent because CADS storage needs to be refilled (Fig. 7b,
negative CADS flow indicate refilling). Therefore, the con-
strained boundary condition (node 6) is still active and con-
duit drawdown recovers with ongoing time in parallel with
refilling the CADS (Fig. 7a, b). If CADS is refilled, the water
deficit is no longer existent and the limited flow boundary at
node 6 switches to fixed head, while matrix heads, and ac-
cordingly matrix transfer and spring flow, recover to the ini-
tial values. Again, these effects are increased with increasing
CADS (Fig. 7a, b).
So far, the analysis demonstrates that both matrix trans-
fer and CADS act in parallel. The sensitivity of model re-
sults on CADS is previously investigated. Matrix transfer can
be controlled by the transfer coefficient αex (Eq. 5). Conse-
quently, the sensitivity of model results on this parameter is
subsequently investigated. For that reason, an initial model
with WCADS = 0.25 m and αex/lp = 1× 10−5 ms−1 is varied
by setting αex/lp to 2×10−5 ms−1 and 5×10−6 ms−1, respec-
tively.
Results are presented in Fig. 8. As already discussed, the
onset of water abstraction results in a water deficit that is bal-
anced by matrix transfer and CADS flow (Fig. 8a, b). An in-
creased transfer coefficient results in increased matrix trans-
fer with simultaneously decreased conduit drawdown (Eq. 5)
and, therefore, decreased CADS flow (Eqs. 6–8). A com-
parable behavior occurs for decreased transfer coefficients
(decreased matrix transfer, increased conduit drawdown, and
increased CADS flow; Fig. 8a, b). The log-log diagnostic
plots (Fig. 8c) are reflecting these characteristics with an in-
creasing amount of fast storage, indicated by the unit slope
of drawdown and drawdown derivative, for decreasing wa-
ter transfer coefficients. Further, the variation of the water
transfer coefficient is sensitive to initial matrix heads and ma-
trix drawdowns (Fig. 8d). In particular, initial matrix heads
are increased for smaller values of αex/lp, which represent
higher hydraulic resistances to matrix–conduit water transfer
and, therefore, correspond to larger differences between ma-
trix and conduit heads. In addition, it may be noted that ini-
tial matrix heads are again independent of changes in WCADS
(cf. Fig. 7d). Matrix drawdown, however, is affected by both
parameters. First, increasing WCADS from 0 to 0.25 m (with
αex/lp = 1× 10−5 ms−1 in both cases) reduces the drawdown
as explained above. Second, variations of αex/lp alone il-
lustrate that matrix drawdown is lowered for smaller values
of this parameter which are also responsible for higher hy-
draulic resistances to matrix–conduit water transfer, i.e., an
increased amount of water is abstracted from CADS during
pumping.
This simplified model study demonstrates the importance
of the CADS concept: without CADS, any water deficit (for
abstraction scenarios) that is not covered by recharge or ex-
ternal boundary condition, e.g., a fixed head, will result in
an immediate change of water transfer between conduits and
matrix continuum that is directly associated with an imme-
diate variation of conduit heads. CADS provides water im-
mediately (for a water deficit) and, therefore, can dampen
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234 T. Reimann et al.: Representation of water abstraction
Fig. 7. Simulation results for the enhanced model (with CADS and FHLQ boundary condition): (a) flow terms for the fixed-head/FHLQ
boundary and conduit heads at node 5; (b) flow terms for matrix transfer and CADS flow; (c) log-log diagnostic plot for conduit drawdown
(solid lines) and drawdown derivative (dashed lines) at node 5; (d) initial matrix head and matrix drawdown at day 4 along the cross section
A–A’ (Fig. 5).
the conduit and matrix head variation. It can be concluded
that CFPM1 with CADS is able to reproduce the charac-
teristic damped-drawdown behavior within conduits in cases
of short- and long-term water abstraction (compare Fig. 1).
Log-log diagnostic plots for conduit drawdown and draw-
down derivative further approve the existence of fast conduit
storage. Overall, CFPM1 with CADS creates testable results.
4 Cent Fonts case study
A highly idealized representation of the Cent Fonts field sit-
uation described by Maréchal et al. (2008) is created to pro-
vide an application outlook for using CFPM1 with CADS
and FHLQ to represent karst water abstraction scenarios. In
doing so, the case study is meant to demonstrate the ability
of CFPM1 to reproduce field observations. Data and parame-
ters used for this idealized model are, in most instances, from
Maréchal et al. (2008). Several scenarios are performed to
investigate parameter sensitivities in response to the onset of
water abstraction.
4.1 Model setup
The basic features of the study area (Fig. 1) are conceptu-
alized for modeling purposes as shown in Fig. 9. Cauchy
boundary conditions are applied at the north and south bor-
ders of the model grid to represent rivers in the catchment
area (Fig. 9). The head-dependent water transfer between
matrix and rivers is approximated by the MODFLOW River
Package with a riverbed conductance of 100 m2 s−1. All
other lateral outer boundaries of the matrix continuum are of
Neumann type (no flow). A uniform diffuse areal recharge of
6.34× 10−9 ms−1 (200 mm a−1) is applied. The matrix hy-
draulic conductivity Km is set to 9.00× 10−6 ms−1 (to ob-
tain adequate matrix hydraulic heads) and matrix storage
is Sm = 0.007 (Maréchal et al., 2008). The matrix contin-
uum is discretized by 85 rows and 35 columns with cell
lengths and widths equal to 100 m x 100 m. Vertically, the
model domain is represented by one unconfined layer with
top = 250 m a.s.l. and bottom =−150 m a.s.l.
Highly conductive karst features are represented by one
central conduit from north to south, which is subdivided into
90 tubes (each approximately 100 m long) and 91 nodes.
CADS is implemented with a width of WCADS = 0.21 m
resulting in a storage area WCADS × lCADS of ∼ 1900 m2
(Maréchal et al., 2008). Conduit node elevation is assumed
Hydrol. Earth Syst. Sci., 18, 227–241, 2014 www.hydrol-earth-syst-sci.net/18/227/2014/
T. Reimann et al.: Representation of water abstraction 235
Fig. 8. Simulation results for the enhanced model (with CADS and FHLQ boundary condition): (a) flow terms for the fixed-head/FHLQ
boundary and conduit heads at node 5; (b) flow terms for matrix transfer and CADS flow; (c) log-log diagnostic plot for conduit drawdown
(solid lines) and drawdown derivative (dashed lines) at node 5; (d) initial matrix head and matrix drawdown at day 4 along the cross section
A-A’ (Fig. 4).
Fig. 9. Conceptual representation of the large-scale pumping test
scenario at the Cent Fonts karst system.
at 0 m a.s.l. The conduit diameter is estimated from spring re-
sponse analysis, according to the concept of Ashton (1966),
to be 3.5 m (Birk and Geyer, 2006). Pipe roughness height
is set to 0.01 m. Water transfer between matrix and conduit
is realized by setting αex for each node to 4.5× 10−5 ms−1.
The water transfer coefficient αex is doubled in node 1
and node 91 to represent the coupling between river and
conduit. The karst spring in the south (node 91) is imple-
mented by an FHLQ boundary condition with fixed head at
76.9 m a.s.l. and inflow limited to 0.03 m3 s−1 (Maréchal et
al., 2008). Water abstraction is realized by pumping from
node 87 at 0.4 m3 s−1 (Fig. 9). Two different time peri-
ods are considered: (1) initial period (steady-state) until
day 6 and (2) pumping from day 6 to day 38. Beyond
the basic model, CADS and conduit–matrix coupling are
varied to obtain first insights into sensitivities. Therefore,
the CADS width WCADS is set to 0.05 and 0.50 m (ba-
sic model 0.21 m), and the water transfer coefficient αex
is varied as 4.0× 10−5 ms−1 and 5.0× 10−5 ms−1 (basic
model 4.5× 10−5 ms−1).
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236 T. Reimann et al.: Representation of water abstraction
Fig. 10. Simulation results for the large-scale pump test scenario: (a) flow terms for variable CADS; (b) flow terms for variable matrix–
conduit transfer; (c) log-log diagnostic plot for conduit drawdown and drawdown derivatives at node 5; (d) initial matrix head and matrix
drawdown at day 38 along the cross section A–A’ (Fig. 9), note that initial heads for models with varying WCADS are the same.
4.2 Results for the idealized model – initial run and
parameter sensitivity
Figure 10 presents flow terms along time, log-log diagnos-
tic plots, and the behavior of matrix heads. In general, wa-
ter abstraction from the conduit produces a relatively con-
stant drawdown in the pumping well. During the beginning
of drawdown formation, CADS flow significantly contributes
to balance the pumping induced water deficit. This results
in smoother conduit drawdown without an immediate head
drop. With ongoing time, CADS flow decreases and matrix
transfer increases (Fig. 10a, b). Consequently, CADS influ-
ences conduit drawdown and drawdown derivatives for early
times much more than matrix transfer. The fast storage, pro-
vided by CADS, is reflected by the unit slopes of drawdown
and drawdown derivative in the log-log diagnostic plots, too
(Fig. 10c). The head gradient within the matrix along cross
section A–A’ (see Fig. 9) is moderate and the matrix draw-
down is less than in the conduit (Fig. 10d).
The general behavior of parameter variation with respect
to CADS (WCADS) and matrix transfer (αex) is as previously
discussed for the simple test model (Sect. 3.2). However, in
the context of this application outlook with parameters ac-
cording to a real situation, it is obvious that the short-term
system reaction on hydraulic stress is much more sensitive
to CADS (Fig. 10a, b). The smaller the CADS the faster the
conduit reaction and the faster a quasi-steady conduit head
is reached (Fig. 10a). Further, the quasi-steady conduit head
depends on the conduit–matrix coupling, here varied via the
transfer coefficient αex (Fig. 10b). In fact, drawdowns in the
conduit pumping well are reduced with better coupling (in-
creased αex) because the necessary head difference between
matrix and conduit to result in a certain water transfer is re-
duced (see also Eq. 5). On the contrary, smaller water transfer
coefficients result in enhanced conduit drawdown (Fig. 10b).
The initial matrix head distribution is sensitive to the trans-
fer coefficient because this parameter regulates flow and head
difference between matrix and conduits (Eq. 5; Fig. 10d).
Further, the current system understanding indicates that the
initial matrix head distribution depends on the spatial distri-
bution of the conduit network and the transfer coefficients.
Due to our conceptual model, the matrix is mainly drained
by conduits and, therefore, variations of αex are strongly af-
fecting matrix heads. Initial matrix heads are not influenced
by CADS because steady-state situations do not account for
storage. However, under the used parameters, matrix draw-
down is sensitive to CADS and clearly decreases with in-
creasing CADS (Fig. 10d) because matrix–conduit trans-
fer and conduit drawdown is decreased (Fig. 10a). Matrix
drawdown is comparatively less sensitive to matrix–conduit
transfer (Fig. 10d).
Hydrol. Earth Syst. Sci., 18, 227–241, 2014 www.hydrol-earth-syst-sci.net/18/227/2014/
T. Reimann et al.: Representation of water abstraction 237
Table 1. Water budget terms for CFPM1 demonstrating the origin of pumped water. All terms are computed based on average values for
period 2.
model run basic CADS decreased CADS increased αex decreased αex increased
spring (FHLQ boundary) 7.5 % 7.5 % 7.5 % 7.5 % 7.5 %
CADS 9.9 % 2.4 % 21.2 % 11.5 % 8.6 %
matrix (all terms) 82.6 % 90.1 % 71.3 % 81.0 % 83.9 %
matrix: from storage 38.2 % 44.0 % 29.0 % 39.3 % 37.0 %
matrix: from recharge 47.1 % 47.1 % 47.1 % 47.1 % 47.1 %
matrix: from river 15.8 % 16.8 % 14.6 % 14.0 % 17.5 %
matrix: to storage 0.0 % 0.0 % 0.0 % 0.0 % 0.0 %
matrix: to river −18.5 % −17.8 % −19.4 % −19.4 % −17.7 %
Water budget terms are given in Table 1. Hence, for the
initial model about 10 % of water pumped during period 2
comes from CADS and about 38 % comes from matrix stor-
age. Further budget terms for the parameter study under-
line the already discussed model behavior. Accordingly, the
amount of pumped water coming from the matrix storage
decreases as CADS increases (Table 1), as expected. Fur-
thermore, the conduit–matrix coupling (αex) does not sig-
nificantly affect the distribution of water coming from CAD
storage and from matrix storage, see Table 1.
In principle, CFPM1 with the CADS and FHLQ function-
ality is able to qualitatively reproduce the field situation de-
scribed by Maréchal et al. (2008) (Fig. 1). It can be concluded
that CADS has a strong influence on model reaction to hy-
draulic stresses like the onset of water abstraction. On the
contrary, matrix–conduit transfer is very sensitive to the ini-
tial matrix heads. Matrix heads and matrix drawdown vary
significantly with distance from the conduit. Consequently,
matrix heads seem to be very valuable to estimate the spatial
distribution of the conduits.
4.3 Comparison with measured data
Subsequently, the model is further adapted according to the
situation described by Maréchal et al. (2008) in order to com-
pare model results with field measurements. The previous
analysis demonstrates that the system strongly reacts to hy-
draulic stress. Because the pumping well is directly placed
in the highly conductive conduit, pumping rate variations are
expected to strongly affect hydraulics. Consequently, mea-
sured pumping rates, slightly variable with time (see Fig. 1
right), are considered by CFP as time-dependent input data
with a resolution of 1t = 3600 s. Further, over period 2
(pumping) the diffuse areal groundwater recharge is reduced
to 10 % of the initial value (6.34× 10−9 ms−1) because the
field experiment was conducted during a dry period with-
out recharge (Maréchal et al., 2008). Here, the remaining
recharge of 6.34× 10−10 ms−1 is assumed as background
value due to slow draining of the less conductive rock matrix.
Two model setups are automatically calibrated using
PEST (Doherty, 2005) whereas Km (matrix hydraulic con-
ductivity, upper and lower boundary 1.00× 10−5 ms−1 and
1.00× 10−8 ms−1), Sm (matrix storage, upper and lower
boundary 2.00× 10−1 and 1.00× 10−4), and αex (transfer
coefficient, upper and lower boundary 1.00× 10−4 m2 s−1
and 1.00× 10−8 m2 s−1) are considered as free parameters.
CADS is not considered for calibration in order to reduce the
number of free parameters. Rather, CADS is parameterized
according to Maréchal et al. (2008). Hence, setup (1) uses
WCADS = 0.21 m. Setup (2) is intended to investigate how
CFP without CADS can reproduce field observations. Con-
sequently, CADS is deactivated by setting WCADS = 0.00.
Calibration considered measured conduit drawdown at the
pumping well (node 87) plus matrix drawdown. Because the
position of matrix drawdown relative to the conduit is un-
known, only a rough estimation of 1hm = 5 m (over the
pumping period) with hm,ini = 110.0 m a.s.l. (Maréchal et al.,
2008) is assumed at position M1 with a distance of 1000 m
between conduit and matrix observation well (Fig. 9).
Computed flow terms and conduit heads are presented in
Fig. 11. In general, both models show similar behavior of
computed and measured conduit drawdown. However, the
model without CADS fails to reproduce periods with highly
variable pumping rate (onset of water abstraction at day 6,
interrupted pumping around day 14) due to the missing fast
storage. On the contrary, CFP with CADS does represent
much better the early stage of the pumping test as well as
the interrupt around day 14. Further, it is obvious that pump-
ing rate variations considerably influence flow terms. For the
CFP model without CADS, matrix–conduit transfer responds
to pumping rate variations. As previously discussed (Sect. 3),
this is closely connected with an immediate conduit head
variation. If CAD storage is accounted for, mainly CADS
flow responds to pumping rate variations whereas matrix–
conduit transfer is basically unaffected. Consequently, the
conduit head drawdown curve is much smoother due to the
CADS caused damping.
The resulting log-log diagnostic plots (Fig. 11b) underline
the significance of CADS in order to represent fast storage
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238 T. Reimann et al.: Representation of water abstraction
Fig. 11. Simulation results for the large-scale pump test scenario: (a) flow terms and conduit heads computed with CFP and CFP/CADS;
(b) computed drawdown in both conduit (solid lines) and matrix (dashed lines) for the basic situation with drawdown derivatives (symbols)
computed according to Eq. (12); (c) computed drawdown in the conduit for varying CADS width and water transfer coefficient.
that results in the unit slopes for conduit drawdown and draw-
down derivative. Keeping in mind that the aim of the simpli-
fied model is to evaluate different model concepts rather than
to find a good fit (which strongly depends on assumptions
on conduit geometry), the deviation between measured and
modeled heads is acceptable for setup (1). Figure 11b also
shows that matrix head drawdown computed at observation
well M1 (for location see Fig. 9) is qualitatively similar to
matrix head drawdowns reported by Maréchal et al. (2008)
as indicated in Fig. 1. Therewith, CFP with CADS is able to
qualitatively describe the drawdown behavior with time for
both conduit and matrix heads. On the contrary, setup (2) is
not able to represent the initial phase of the pumping test as
well as the reaction of conduit heads on strong variations of
the pumping rate because the model lacks CADS (Fig. 11a,
b). This produces the already described instantaneous drop
of conduit heads missing the initial period of unit conduit
drawdown and drawdown derivative (Fig. 11b).
The matrix heads prior to pumping as well as the
drawdown after 38 days of pumping along the A–A’
cross section are shown in Fig. 11c. Due to the in-
creased transfer coefficient in setup (2), the initial hy-
draulic gradient within the matrix is more pronounced.
Because setup (2) lacks CADS, the matrix drawdown
is increased, too. The following parameters are obtained
after calibration: for setup (1) with WCADS = 0.21 m:
αex = 8.72× 10−5 m2 s−1, Km = 3.00× 10−6 ms−1, Sm =
0.0011; for setup (2) with WCADS = 0.00 m: αex = 2.85
× 10−4 m2 s−1, Km = 1.00× 10−6 m s−1, Sm = 0.0007. As
the model without CADS needs to infer matrix–conduit
transfer to respond to pumping induced hydraulic stress
(Fig. 11a), αex is increased to achieve a better conduit–matrix
coupling. Further, Km as well as Sm are decreased to increase
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T. Reimann et al.: Representation of water abstraction 239
the matrix responding behavior of the model without CADS.
Therewith, the gradient of matrix heads is steeper and matrix
head drawdown is increased (Fig. 11c).
Finally, it can be summarized that CFP with CADS is a
suitable tool to represent karst catchments under water ab-
straction (and other hydraulic stresses). Thereby, CADS is
necessary to account for the fast storage component associ-
ated with conduits that results in non-abrupt drawdown of
conduit heads. Further, the case study highlights that matrix
heads are sensitive to (a) the transfer coefficient, (b) the dis-
tance from the conduit as well as (c) CADS (Fig. 11). Several
modifications appear to be possible to achieve further model
improvement, for example a more realistic consideration of
the model domain geometry, the local geology, and the dis-
tribution of karst conduits within the matrix. This may help
to further reduce deviations between modeled and measured
conduit heads (Fig. 11a). Additional analysis can be applied
for further model evaluation like flow dimension analysis as
indicated by, for example, Walker et al. (2003), Maréchal et
al. (2008), and Cello et al. (2009).
5 Conclusions
Implementation of conduit-associated drainable storage
(CADS) to the existing Conduit Flow Process Mode 1
(CFPM1) combines the conceptual approaches for water
storage in karst systems presented by Mangin (1975, 1994)
and Drogue (1974, 1992) resulting in a triple porosity sys-
tem representation (Worthington et al., 2000). Thereby, ma-
trix and fracture porosity are usually merged within one con-
tinuum because an REV can be defined. Hydraulic parame-
ters of the REV (fissured/fractured matrix blocks) can be ob-
tained from traditional hydraulic borehole tests (e.g., Geyer
et al., 2013). Fast reacting conduit-associated storage is rep-
resented by CADS. The newly developed functionality is
fully integrated in the CFPM1 flow subroutines and requires
only the storage width as an additional model parameter. The
CADS volume (parameterized by the CADS width WCADS)
is a calibration parameter with a physical background and
can be obtained via transient model calibration, for example,
from the reaction of conduit heads on hydraulic stresses like
start of pumping, stop of pumping, or strong recharge signals
directly routed in the conduits. As CADS volume is concep-
tually independent from the conduit volume, the chosen ap-
proach allows a rather flexible treatment of water storage or
release behavior linked to the highly permeable flow system.
The CADS approach was evaluated in several pumping
test scenarios to investigate the effect of storage properties
and boundary conditions on karst hydraulics. Simulation re-
sults show that associated conduit storage plays a major role
during the early time periods of water abstraction from karst
systems, even though the majority of total aquifer storage
is provided by the matrix storage. This is primarily due to
the fact that only a small amount of water from matrix stor-
age is provided during the early stages of water abstraction
through conduit–matrix coupling. The newly implemented
CADS flattens the drawdown curve from the beginning of
water abstraction from the conduit system because of imme-
diate water inflow from CAD storage.
Depending on the model setup, strong water abstraction
within highly permeable structures, i.e., conduits, can re-
sult in unhampered water inflow through fixed-head bound-
aries connected to the pipe network. This effect leads to mi-
nor drawdown during water abstraction even at high pump-
ing rates and consequently an insignificant contribution from
the CADS. This condition can be relevant, for example, for
streams that are hydraulically perfectly connected to karst
conduit systems. Therefore, the simulation of pumping tests
with CFPM1 can require the additional implementation of a
fixed-head limited-flow (FHLQ) boundary condition, which
constrains inflow for constant head boundaries. For these sce-
narios, water deficit resulting from water abstraction from
the conduit system is balanced out by contributions from the
CADS and the matrix storage.
CADS is assumed to be uniform (width is constant
with depth). Furthermore, groundwater flow within CADS
(e.g., horizontal or vertical flow driven by hydraulic gradients
within the pipe) is not represented. Wellbore storage also is
not considered by CADS, however, the parameters of CADS
may be adjusted during calibration to account for wellbore
storage. CADS and CFPM1 updates that overcome these lim-
itations will eventually be available under the subsequently
provided internet domain.
CADS and the FHLQ boundary were further evaluated
to simulate a large-scale field pumping test reported by
Maréchal et al. (2008). Dimensions and hydraulic model pa-
rameters were set in the range of observed field values. Even
though the geometry of the karst aquifer was highly ideal-
ized, the model was able to qualitatively reproduce the over-
all drawdown curves observed in the pumping well and the
observation wells. Initial comparison of computed and mea-
sured drawdown demonstrates the necessity of fast storage
associated with conduits. Ongoing work will evaluate the
large-scale pumping test with CFPM1 and CADS by us-
ing an adequate hydrogeological representation of the catch-
ment and further diagnostic tools like drawdown derivatives
and flow dimension analysis. Further work will focus on
systematic-type curve analyses to evaluate pumping test re-
sponses under different complex modeling setups. The newly
developed CADS package and FHLQ boundary can be used
for evaluation of large-scale karst aquifer hydraulic tests
with relatively modest input data requirements. Further, even
more ambitious studies concerning, for instance, spatially or
temporally variable recharge or hydraulic and hydrochem-
ical responses of karst springs as outlined by Hartmann et
al. (2012, 2013) or Long and Mahler (2013) appear to be
feasible in the long run.
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240 T. Reimann et al.: Representation of water abstraction
Acknowledgements. This project was funded by the Deutsche
Forschungsgemeinschaft (DFG) under Grants no. LI 727/11-2 and
GE 2173/2-2 and by the B.R.G.M. under Grant no. PDR13D3E91.
We acknowledge support by the Open Access Publication Funds of
the TU Dresden.
The executable of CFPM1 with CADS together with an
extensive documentation is available under the internet domain
http://www.tu-dresden.de/fghhigw (download section).
Edited by: J. Carrera
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