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Storage and release of conservative solute between karst conduit and fissures using a laboratory analog

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The contaminant transport processes in karst water systems have a direct impact on the quality and utilization of karst water resources. The storage and release of contaminants or conservative solutes during the solute transport process is a common phenomenon in karst aquifers. The impact of the storage and release is more prevalent after focused recharge events. In this study, laboratory experimental and numerical studies were conducted to quantify the storage and release processes of conservative solute. The results showed that, conduit water recharges into fissures under high water head conditions, and the fissure water drains back into the conduit while the hydraulic gradient reverse. The conservative solute storage-release process controlled by hydrodynamic conditions produces strong asymmetry, long tailing, or bi-peak in the breakthrough curves (BTCs). The BTCs change from single peak to bi-peak with enhanced hydrodynamics under focused recharge conditions. The dual heterogeneous domain model was calibrated to simulate the long-tailing of the BTCs and their noticeably bimodal characteristics. The flow velocity and dispersion coefficient are the major variables that regulate the bimodal structure of the BTCs, which also control the solute storage-release differences between the conduit and fissures. The bimodal structure of the BTCs becomes more pronounced for large discrepancies in flow velocities. The total BTCs are a superposition of solute transport in the conduit path and storage-release path. A method to evaluate the mass of conservative solute transport in storage-release paths was proposed by segmenting the transport curve in the conduit from the total BTCs, thus quantifying the effects of the groundwater storage-release mechanism on the solute transport process in the karst water system.
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Journal of Hydrology 612 (2022) 128228
Available online 22 July 2022
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Research papers
Storage and release of conservative solute between karst conduit and
ssures using a laboratory analog
Huaisong Ji
a
, Mingming Luo
a
,
*
, Maosheng Yin
b
, Chenggen Li
a
, Li Wan
a
, Kun Huang
a
a
School of Environmental Studies, China University of Geosciences, Wuhan, Hubei 430078, China
b
School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
ARTICLE INFO
This manuscript was handled by Corrado Cor-
radini, Editor-in-Chief, with the assistance of
Yongjun Jiang, Associate Editor
Keywords:
Karst water system
Conduit and ssures
Conservative solute
Storage-release
Laboratory experiment
ABSTRACT
The contaminant transport processes in karst water systems have a direct impact on the quality and utilization of
karst water resources. The storage and release of contaminants or conservative solutes during the solute transport
process is a common phenomenon in karst aquifers. The impact of the storage and release is more prevalent after
focused recharge events. In this study, laboratory experimental and numerical studies were conducted to
quantify the storage and release processes of conservative solute. The results showed that, conduit water re-
charges into ssures under high water head conditions, and the ssure water drains back into the conduit while
the hydraulic gradient reverse. The conservative solute storage-release process controlled by hydrodynamic
conditions produces strong asymmetry, long tailing, or bi-peak in the breakthrough curves (BTCs). The BTCs
change from single peak to bi-peak with enhanced hydrodynamics under focused recharge conditions. The dual
heterogeneous domain model was calibrated to simulate the long-tailing of the BTCs and their noticeably
bimodal characteristics. The ow velocity and dispersion coefcient are the major variables that regulate the
bimodal structure of the BTCs, which also control the solute storage-release differences between the conduit and
ssures. The bimodal structure of the BTCs becomes more pronounced for large discrepancies in ow velocities.
The total BTCs are a superposition of solute transport in the conduit path and storage-release path. A method to
evaluate the mass of conservative solute transport in storage-release paths was proposed by segmenting the
transport curve in the conduit from the total BTCs, thus quantifying the effects of the groundwater storage-
release mechanism on the solute transport process in the karst water system.
1. Introduction
Karst aquifers cover approximately 20 % of the worlds land area and
are an important source of drinking water for approximately 25 % of the
global population (Ford and Williams, 2013). Despite the signicance of
karst water resources, there are a growing number of contamination
incidences in karst aquifers worldwide (Henry and Suk, 2018). It is well
known that strong karstication not only creates a special karst land-
scape on the surface, but also creates a multi-layer structure on both the
surface and underground. The surface karst has rapid inltration with
very low ltration and storage capacity, making the karst aquifer
extremely vulnerable to the surface-related contaminants (Goeppert and
Goldscheider, 2019; Lu et al., 2013; Lasagna et al., 2013). More
importantly, contamination can intensively get into the karst aquifers
through surface runoff or overland ow that conuences in negative
terrains, such as karst depressions, dolines, and sinkholes (Fig. 1) (Guo
et al., 2010; Jakada et al., 2019; Vadillo and Ojeda, 2022; White et al.,
2018).
In many instances, the impact of such focused recharge on karst
groundwater quality remains poorly understood, and the risk of
groundwater contamination is widely underestimated because of the
fast ow into aquifers (Hao et al., 2021; Medici and West, 2021). It is
also common for residents to use karst depressions and sinkholes as
refuse dumps, resulting in unltered short-lived contamination into
karst aquifer, causing catastrophic groundwater pollution (Jakada et al.,
2019; Zhou et al., 2018). Furthermore, extreme weather events have led
to more frequent and intense ooding events in karst areas (Wang and
Chen, 2021). These phenomena make it difcult to prevent sudden
pollution incidents caused by short-term pulses of contamination input
(Zhang et al., 2020). Previous studies have revealed that focused
recharge is the primary reason for widespread rapid transport of con-
taminants into the karst groundwater (Hartmann et al., 2021).
* Corresponding author.
E-mail address: luomingming@cug.edu.cn (M. Luo).
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
https://doi.org/10.1016/j.jhydrol.2022.128228
Received 27 April 2022; Received in revised form 11 July 2022; Accepted 13 July 2022
Journal of Hydrology 612 (2022) 128228
2
Conservative solutes are those that do not react chemically or bio-
logically during solute transport process (Khosronejad et al., 2016;
Lamberti and Hauer, 2017). Quantitative conservative tracer tests have
been widely employed to analyze hydraulic characteristics and identify
contaminant sources in karst aquifers (Bailly-Comte and Pistre, 2021;
Benischke, 2021; Goldscheider and Drew, 2007; Mohammadi et al.,
2021a; Schiperski et al., 2022). These conservative tracer tests showed
that aquifer heterogeneity generates anomalous transport (Goeppert
et al., 2020; Molinari et al., 2015). Consequently, the tracer transport
process and its accompanying morphology of BTCs are complicated and
variable, making the interpretation of results ambiguous and requiring
multiple solutions.
For example, most previous studies have attributed the observed
single-peak tailing BTCs to the interactions with pools or immobile
zones along the main conduit (Dewaide et al., 2016; Goldscheider, 2008;
Wu et al., 2020; Zhao et al., 2021, Zhao et al., 2019). Meanwhile the bi-
peak tailing BTCs generated by a single recharge event have been
interpreted with reference to underground lakes, auxiliary conduits,
multiple conduit congurations, or aquifer medium types, and have
been veried by laboratory experiments and numerical simulations (Cen
et al., 2021; Chu et al., 2021; Dewaide et al., 2018; Field and Leij, 2012;
Goldscheider et al., 2008; Perrin and Luetscher, 2008; Tinet et al., 2019;
Wang et al., 2020; Wu et al., 2021).
However, there is also the possibility that the inversion of the hy-
draulic gradient between the conduit and the ssures network could
produce anomalous transport of conservative solutes (Faulkner et al,
2009; Goeppert et al., 2020; Zhang et al., 2020), while this process has
not been veried due to the complex eld conditions and many inu-
encing factors (Richter et al., 2022; Sivelle and Labat, 2019). How does
groundwater storage and release processes affect the transport of con-
servative solutes under focused recharge conditions? What will be the
morphology of BTCs at the outlet of karst springs? These are important
questions that should be addressed.
Therefore, it is important to critically study the behavior of conser-
vative solutes in karst groundwater under focused recharge conditions
to better understand the processes of solute transport, storage and
release. Here, we evaluated the mechanisms of eld scale storage and
release of solutes under high and low ow conditions with focused
recharge. Laboratory scale models were employed to allow better in-
sights into groundwater ow and solute transport under controlled
conditions (Mohammadi et al., 2021b). In this work, a laboratory-scale
physical model was employed to investigate the solute transport in a
conduit-ssure system under high and low ow conditions with focused
recharge.
Existing solute transport models cannot capture both the heteroge-
neity in mobile domains and the bi-peak characterized by the long-
tailing of BTCs observed in complex media solute transport experi-
ments. For example, the advectiondispersion equation model (ADE)
has been used for approximately-ve decades to model solute transport
in karst water system (Li et al., 2020). However, the ADE model fails to
characterize bi-peak BTCs, and is not suited to capture the mass transfer
process between immobile zones such as pools or eddies and conduits.
Recently, Goeppert et al. (2020) applied the continuous time random
walk (CTRW) theory to account for the long-tailed breakthrough be-
haviors found in karst water system. To integrate the effect of auxiliary
conduits in generating multi-peaks BTCs, Field and Leij. (2012) have
proposed a dual-advection dispersion equation (DADE) that efciently
reproduces multi-peaks BTCs. However, this model does not allow for
discreet allocation of the conduits along with the ow or combine the
two exchange advectivedispersive zones with a storage area. Wang
et al. (2020) reexamined the ability of the DADE model to reproduce
BTCs with a single peak and bi-peak in a dual conduit structure, and they
discovered that the model did not reproduce the skewness of some parts
of the slower peaks.
To characterize the conservative solute transport process, a solute
transport model that can capture the heterogeneity in mobile domains,
exhibiting bi-peaks and characterized by late-time tails was calibrated.
This model was applied to elucidate the characteristics of conservative
solute transport in a heterogeneous karst water system. The high reso-
lution of laboratory-scale tracer tests and the reliability of the simulation
Fig. 1. Pollution characteristics of karst groundwater under focused recharge condition (modied after Zhou et al., 2018).
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
3
results allow us to provide new insights into the conservative solute
transport generated by groundwater storage and release processes in
karst water systems. These outcomes provide a scientic basis for the
better development and utilization of karst water resources, as well as
the protection and conservation of its ecosystems.
2. Materials and methods
2.1. Conceptual model of solute storage and release in eld-scale
In highly karstied area, surface water and groundwater are always
connected through sinkholes and karst conduits. Those karst aquifers
with conduits and ssures, and the conduits lie over an aquitard which
are very common in sedimentary stratiform karst aquifers in South
China (Fig. 1, Fig. 2). After rainstorms, quick hydrological responses will
occur in karst springs, leading to rapid increases in the water level of the
underground river channels or karst conduits. Runoff accumulates when
it reaches the sinkholes as the karst network becomes fully saturated and
its drainage capacity is surpassed, resulting in in-situ ooding (Luo et al.,
2016; Gil-M´
arquez et al., 2019; Naughton et al., 2018). In such situa-
tions, groundwater-borne solutes are transported rapidly through a
network of karst conduits, undergoing frequent and rapid exchanges
with ssures in response to the hydraulic gradient (Binet et al., 2017;
Shu et al., 2020; Zhao et al., 2022).
As shown in Fig. 2a, during short-interval rainstorms, the conduit
rapidly recharges via sinkholes. Given the limited drainage capacity of
the conduit, water levels increase rapidly, reaching levels higher than
those in ssures, which would drive the conduit-borne solutes both in
the unsaturated and saturated zone owing into the surrounding ssures
for storage. When the rainfall ceases, the conduits hydraulic head di-
minishes due to the recharge recession and becomes inverted, thereby
mobilizing the groundwater stored in ssures, pushing the stored solutes
from ssures into conduits (Fig. 2b) (Chang et al., 2021; Faulkner et al.,
2009; Kalantari and Rouhi, 2019; Li et al., 2008; Shirafkan et al., 2021).
2.2. Construction of the laboratory-scale physical model
According to the eld-scale model (Fig. 2), the conceptual model of
this experiment is based on the hydrological conditions in the eld. The
simplied conceptual model presented in this work represents those
karst aquifers with conduits and ssures. The special hydrogeological
structure makes the transport paths of solutes injected through the
sinkholes after rainstorms which can be presented in two categories:1)
solutes directly transported from the sinkhole to spring outlet along the
conduit without exchange with the surrounding ssures; 2) solutes are
stored in the ssures during high ow conditions and released back into
the conduit during low ow conditions.
In this study, a two-dimensional experiment apparatus was
constructed based on this summarized conceptual model (Fig. 3). The
experiment apparatus consists of three units: the focused recharge and
tracer injection system, the conduit and ssure system, and the data
monitoring and acquisition system.
The focused recharge unit is a cube tank (36 cm length ×36 cm
width ×45 cm height) with a vertical circular conduit connected to the
bottom of the tank to simulate a depressional catchment and sinkhole.
The vertical conduit is connected to the tracer injection unit which also
regulates the focused recharge water and tracer injection ow rate via
control valves. A rectangular plexiglass box was used to create a lling
slot with dimensions of 100 cm ×15 cm ×40 cm (length ×width ×
height) for the conduit and ssure system. The horizontal circular
conduit, with a length of 100 cm and an inner diameter of 4 cm, is placed
at the bottom of the plexiglass box. 840 boreholes (8 rows of 105 each)
are drilled above the halfway point along the horizontal conduit. The
boreholes are 3 mm inner diameter and 9 mm apart to provide water
exchange channels between the conduit and ssures. The conduit was
sealed at other points to the ssures to avoid for circulations at the
border between ssures and conduit.
To mimic a karst conduit and ssures system in which conduits lie on
an aquitard, a ssure is made of concrete blocks overlying the conduit,
occupying the remaining space of the lling slot. The ssures with width
of 3 to 6 mm were made between the blocks, and the block surface is
rough and contains lots of pores. The void volume of the ssures and
pores accounts for ~ 25 % of the entire volume of the plexiglass box. On
the bottom and back of the lling slot, 40 piezometers are inserted at
various locations. The piezometers are used to measure the water head
pressure at a specic point, and the ow meter can monitor the recharge
of the input conduit and ssure system.
2.3. Tracer test
The experiment apparatus (Fig. 3) is used to conduct tracer tests and
characterize the solute storage-release process. Control valve 4 was set
as a smaller aperture than valve 2 to guarantee that the hydraulic
gradient drives the conduit-water into ssure for storage in the early
stages and the ssure-water can be released back into conduit at a later
time. NaCl was used as a conservative solute (do not react chemically or
biologically) to conduct the tracer tests. At the start of the experiment, a
specic volume of tap water (e.g., 9.0 L, 11.0 L, 13.0 L, 19.5 L, 26.0 L,
and 32.5 L) and equal volume (0.25 L) and equal mass concentration
(60 g/L) of NaCl solution were placed in the tap water tank and the salty
water tank, respectively. For each group of tracer tests, the tap water
was drained by opening control valve 2. Then control valve 1 was also
opened and the injection of 0.25 L NaCl with concentration of 60 g/L
was completed in 50 s with an average injection velocity of 0.1 m/s.
The total duration times of each group tracer tests were completed in
780 to 1730 s. The tracer was injected at the beginning of each group
Fig. 2. Two solute transport paths in the karst conduit-ssure system under focused recharge conditions (modied after Gil-M´
arquez et al., 2019). (a) the water level
in conduit is higher than that in ssures; the conduit-borne solutes permeate the surrounding ssures, (b) the water level in conduit is lower than that in ssures, the
solutes in ssures can be slowly released back into conduit.
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
4
tracer test within 50 s, so the tracer injection is considered as an
instantaneous input compared to the much longer duration time. After
the entire tap water tank was wholly drained, additional water was
added to the tap water tank, which acted as a base ow to maintain the
conduit be full of water during the entire experiment duration. The
tracer concentration was measured indirectly by an electrical conduc-
tivity (EC) instrument (LTC M10 Solinst, Canada) that was placed at the
outlet, with a resolution of ±0.1
μ
S/cm and a recording interval of 5 s.
The concentration of NaCl was converted by EC values using the linear
equation. The EC of the tap water is 300
μ
S/cm, and this value was
deducted in the calibration process. The inuence of different focused
recharge volumes (FRVs) on the solute storage-release process between
the conduit and ssures was investigated using six groups of tracer ex-
periments. To validate the experimental results, each tracer experiment
was replicated three times that reaches the error analysis better than 5
%, and one group of the typical BTCs was chosen for the following
analysis.
2.4. Modelling and calculation
The transport phenomenon of conservative solutes in karst aquifers
after a focused recharge event is complex. Particularly, part of the solute
directly transports through the main conduit with a high ow velocity
with no exchange with the surrounding ssures, while other parts of the
solutes are stored in ssures or matrix and released at a later time due to
the change in hydraulic gradient. There are two different ow paths,
simultaneously operating during solute transport in karst aquifers. So-
lute retention may also be a factor, due to the immobile zone can be
composed of disconnected ssures, porous rock matrix or other stagnant
water zones (e.g., pool volumes) adjacent to the conduits in the natural
karst aquifer. In the laboratory experiment, pores between blocks with
rough surface can mimic the complex ssure network (include the dead-
end ssures) in the karst aquifer. Additionally, there are lots of pores in
the blocks that can act as immobile zone during solute transport (Fig. 4).
To capture such a bimodal sub-diffusion process, the dual hetero-
geneous domain model (DHDM) was augmented in this study, initially
Fig. 3. Schematic diagram of experiment apparatus.
Fig. 4. Schematic diagram of the DHDM model; the ssure-scale consists of multiple embedded local heterogeneous regions; the conduit-scale still presents some
macroscopic heterogeneities.
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
5
proposed by Yin et al. (2020):
C1
t+β1
γ1C1
tγ1=L1(x)C1+k
φ1
(C2C1)(1a)
C2
t+β2
γ2C2
tγ2=L2(x)C2+k
φ2
(C1C2)(1b)
where Ci [ML
-3
] (i =1, 2) is the concentration in domain i; t [T] is time
and x [L] is space coordinate; φi [dimensionless] is the volume fraction
of the i-th domain; the operator Li(x) = vi
x+Di
2
x2 and vi [LT
1
] is the
effective velocity in the i-th domain (vi is typically called the average
linear velocity or seepage velocity for groundwater in the hydrogeology
community, which is equal to the Darcy velocity divided by the effective
porosity); Di [L
2
T
1
] is the diffusion coefcient; k [T
1
] is the rst-order
rate coefcient for mass transfer; βi [Tγi1] is the fractional capacity
coefcient in the i-th domain; and γi [dimensionless] is the time index
representing the degree of time nonlocality for solute transport in the i-
th domain.
The anomalous transport induced by groundwater storage-release is
quite complex, with high transition and difcult to attain entire simu-
lation. After focused recharge and solute injection in the tracer test, the
solute particles may transport along two different paths. Additionally,
an immobile zone may exist and cause solute retention during solute
transport through two paths. As shown in Equation (1), DHDM con-
ceptualizes the aquifer into two mobile domains with different velocities
and hydraulic dispersions to capture solute transport in the two-path
system.
The time-fractional derivative in Equation (1) enables DHDM the
capacity for simulation of solute retention induced by immobile zone.
For simplicity and applicability, constant ow velocity and dispersion
coefcient were used as effective parameters in the DHDM. An explicit
Lagrange scheme can be used to solve Equation (1). The details for
solving scheme for Equation (1) are documented by Yin et al. (2020).
Consistent with the tracer experiment, free ux conditions are used at
the upstream and downstream boundaries. For our scheme, the instan-
taneous release of solute at the beginning was used to simulate the in-
jection of tracers and the mass ux density at the outlet was calculated
by:
Cf(x,
τ
) = pNtotal t2
t1δxXp(t)dt
Ntotal
(2)
where Cf(x,
τ
)[dimenionless] is the normalized mass ux from time t1 to
t2. δ is a Dirac delta function, and XP(t)is the location of particle p at time
t. Ntotal[dimenionless] is the total number of particles in the domains.
The Nash-Sutcliffe Coefcient of Efciency (NSE) (Nash and Sut-
cliffe, 1970) and the Root Mean Square Error (RMSE) was selected as the
criteria for observations and DHDM simulation comparison, which were
dened respectively as:
NSE =1n
i=1yo,iys,i2
n
i=1yo,iy2(3)
RMSE =
1
n
n
i=1yo,iys,i2
(4)
where yo,i and ys,i are the observed and simulated mass ux at the time ti,
respectively, and y is the mean observed mass ux. Under this criterion,
the optimum score of NSE is 1; if NSE 0.5, the simulation can be
considered acceptable; if NSE 0.65, the model is deemed satisfactory;
if NSE 0.75, the model is considered to perform optimally (Morales
et al., 2007). The optimum score of RMSE is equal to 0 when the
simulated values robustly capture the observed values, e.g., the best
model.
3. Results and discussion
3.1. Development in shape of conservative solute BTCs
The observed BTCs with different focused recharge volumes (FRVs)
are depicted in Fig. 5a. The base ow is 22.0 mL/s before the inow of
focused recharge. A small FRV (e.g., 9.0L) exhibits a single, broad peak
with a relatively truncated tailing and asymmetrical form in the BTC.
Note that, the BTC exhibits a development to a bi-peak shape with an
FRV of 11.0L. The corresponding BTCs are all bi-peak curves, with the
FRVs larger than 11.0L. A comparison of the four bi-peak curves shows
that, as the FRV increases, the rst peak displays more symmetry, fol-
lowed by a lag by the second peak, and thereafter, the two peaks become
increasingly separated (Fig. 5a).
As the FRV increases, the BTCs shapes change from a single peak to
bi-peak. The rst peak and the second peak concentration values (Cpeak1
and Cpeak2) show a downward trend. The shape of the second peak curve
is atter and wider compared to the rst peak curve, and all the BTCs
present a noticeable tailing phenomenon. The solute recovery rates (R)
range from 80 % to 95 %, indicating the quality loss of some solutes
(Fig. 5b). Further data regarding the tracer experiments are given in
Table 1.
3.2. Water storage and release processes in ssures
The unitary hydrograph at the conduit outlet is a comprehensive
response to the single recharge episodes from tap water. The ground-
water ow and solute transport process could be explained quantita-
tively by analyzing the hydrographs and associated tracer BTCs. The
calculation for average Reynolds number (Re) is documented by Wang
et al. (2020). The Re of all experiments are larger than 2000, indicating
the turbulent ow conditions, while it is well known that turbulent ow
often occurs in natural karst systems (Worthington and Soley, 2017).
The pressure head variations in the tap water tank and conduit as
well as the outlet discharge processes were observed in all the experi-
ments (Fig. 6 and Fig. 7a). The hydrological process curves are illus-
trative of the salient impacts of hydrodynamic conditions on solute
storage-release processes. Based on the temporal turning points of the
hydraulic head and outlet discharge variations, it is feasible to differ-
entiate between the periods when water is stored and released from the
ssures. The outlet discharge process follows a similar pattern and can
be separated into three stages as shown in Fig. 7.
The outlet discharge increases steadily after focused recharge release
at stage I (Fig. 7b). Considerable focused recharge water creates a rapid
pressurized ow in the conduit. Besides, a limited outlet aperture size
induces parts of the water in conduit store into the ssures due to higher
hydraulic head in conduit than that of ssures. This process increases the
water volume in the conduit-ssures system, and the remainder of the
water is discharged through the conduit outlet. For instance, when FRV
is changed drastically from 9.0 to 32.5 L, the water head (H) in the
ssures also increases from 8.6 to 29.2 cm. Concurrently, the hydraulic
head in the conduit and ssure are superimposed and transferred to the
outlet, triggering the discharge to reach its peak values at the outlet.
Therefore, an increase in hydrodynamic conditions clearly causes an
increase in the storage time and outlet discharge at stage I (e.g., the ow
rate of peak discharge (Qpeak) increases from 31.2 to 36.5 L/s; the storage
time of ssures gets water from conduit (tI) increases from 75 to 185 s)
as shown in Fig. 7a and Table 1.
In stage II, the conduit hydraulic head diminishes due to the focused
recharge recession (Fig. 6a). During this period, the hydraulic gradients
reversed, with the hydraulic gradients in ssures being larger than the
conduit. Subsequently, the outlet discharges steadily decreased after
reaching its peak. At this instance, the focused recharge is not yet
nished, and the outlet discharge mainly consumes the focused recharge
water. Data in Table 1 and Table 2 clearly indicate that, when the FRV is
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
6
small (e.g., 9.0 L), the hydraulic head of the conduit is insufcient to
sustain more water storage in the ssure, resulting in less water (e.g., the
water volume stored in the ssures (Vs) =2.8 L) and solutes entering the
ssures causing the hydraulic head in the conduit to have a shorter
duration (e.g. the total time of focused recharge (tFR ) =85 s), so the
solute retention time (e.g., tII =10 s) in the ssures is also relatively
short.
The velocity of solute transport in conduit is relatively slow for the
9.0 L FRV compared to other scenarios. Hence, there occurred the
mixing processes of solute released by the storage-release path and
conduit transport path, resulting in a single peak tailing curve. However,
when the FRV is larger, the volume of water owing into the ssure
increases. The hydraulic head in the conduit is maintained and extended
by strong hydrodynamic conditions, which can cause solute retention in
the ssures for a longer time (e.g.,tII increases from 25 to 405 s) before
being released. Furthermore, this phenomenon makes the average ow
velocity decline gradually, thus prolonging the time that it takes for the
solute to discharge from an outlet. Ultimately, with the lagged arrival of
Fig. 5. (a) Solute BTCs at the conduit outlet respond to varying FRVs. (b) Solute recovery rate accumulation curve under different focused recharge conditions.
Table 1
Characteristic parameters of the six groups tracer tests.
FRV (L) Cpeak1(g/L) Cpeak2(g/L) tpeak1(s) tpeak2(s) Qpeak(mL/s) tI(s) tII tFR(s) tIII T H R
(s) (s) (s) (cm) (%)
9.0 2.23 115 31.2 75 10 85 695 780 8.6 95
11.0 2.38 0.78 100 240 32.1 90 25 115 855 970 9.7 91
13.0 2.30 0.78 95 320 33.0 100 60 170 830 1000 11.5 86
19.5 1.93 0.56 95 560 33.4 130 150 280 1130 1410 16.2 83
26.0 2.18 0.59 85 810 35.0 150 290 440 1150 1590 23.0 82
32.5 2.12 0.46 90 1020 36.5 185 405 590 1140 1730 29.2 80
Note: Cpeak1: the rst peak concentration value; Cpeak2: the second peak concentration value; tpeak1 and tpeak2: the time corresponding to the rst and second peak
concentrations values, respectively; Qpeak: the ow rate of peak discharge; t
I
: the storage time of ssures get water from conduit; t
II
: the retention time of hydraulic head
maintain stable in conduit; t
FR
: the total time of focused recharge; t
III
: the recession time of ssures water release to conduit; T: the total time of tracer test; H: the
maximum water head in the ssures; R: the solute recovery rates.
Fig. 6. (a) The recharge hydraulic head recession curves in the tap water tank. (b)The hydraulic head curves in the conduit under different FRVs.
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
7
the second peak, the two peaks become progressively separated and
Cpeak2 tend to decrease due to the inuence of mechanical dispersion and
the solute dilution.
As for the release of ssure water following the termination of
focused recharge occurring in stage III during the recession, storage
water is released from the ssures and back into the conduit. Similarly,
the conduit acts as the water transmission channel. At this point, the
outlet discharge consumes only the initial storage water in the ssures.
The outlet discharge gradually decreases until the base ow as the
storage water is gradually discharged from the ssures.
Recession curves are typically plotted in log Q-t space to illustrate the
division of sub-recession curves and calculate the recession coefcient.
Sub-recession curves are plotted as straight lines in log Q-t space when
the spring discharge decreases exponentially (Amit et al., 2002; Tang
et al., 2016). The calculations demonstrate that the recession process of
outlet discharge follows an exponential recessing law (Fig. 7b), with a
Fig. 7. (a) Outlet discharge curves for the experiments under different FRVs. (b) The outlet discharge curve (black line) and recession curve with FRV of 19.5 L on the
log Q-t plot (blue line); the slope of the straight line (pink) is the recession coefcient
α
. I: the water storage stage; II: the recharge retention stage due to increased
FRV; III: the ssures water release stage. (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article.)
Table 2
Calculation of water volumes and hydraulic parameters for the six groups experiments.
FRV (L) v Re
α
Vs Vr Vc VL Vr:FRV Vc:FRV VL:FRV
(m/s) (-) (s
1
) (L) (L) (L) (L) (%) (%) (%)
9.0 1.25 2198 1.176 ×10
-4
2.8 2.5 6.3 0.3 27 69 3
11.0 1.25 2196 1.182 ×10
-4
3.3 2.9 7.7 0.4 27 70 3
13.0 1.26 2216 1.079 ×10
-4
4.0 3.6 9.0 0.4 28 69 3
19.5 1.27 2230 1.211 ×10
-4
5.7 5.1 13.8 0.6 26 71 3
26.0 1.34 2347 1.283 ×10
-4
8.1 7.3 17.9 0.8 28 69 3
32.5 1.40 2457 1.379 ×10
-4
10.2 9.3 22.3 0.9 29 68 3
Note: v: the average ow velocity; Re: the average Reynolds number;
α
: the discharge recession coefcient; Vs: the water volume stored in the ssures; Vr: the water
volume released from the ssures; Vc: the volume of water transported only via conduit; VL: the lost volume of water.
Fig. 8. (a)Variations in the volumes of water transported via different pathways with focused recharge. (b) The proportion of water volumes transported via different
pathways to focused recharge volumes. FRV=V
s+Vc; VL=Vs-Vr.
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
8
relatively stable recession coefcient (
α
) ranging from 1.079 ×10
-4
to
1.379 ×10
-4
(Table 2). The outlet discharge recession time (tIII ) in-
creases from 695 to 1140 s as the FRVs increases.
According to the water balance theory, the results show that, as the
FRV increases, both the water volume released from the ssures (Vr) and
the volume of water transported only via conduit (Vc) rise from 2.5 to
9.3 L, and 6.3 to 22.3 L, respectively (Table 2). The Vs, Vr and Vc with
increased focused recharge show signicant linear positive relationships
(Fig. 8a). However, there is an interesting phenomenon that the pro-
portions of both FRVs are essentially steady, with Vr accounting for ~
27 % (Vr:FRV) of the FRVs on average, while Vc accounts for ~ 70 %
(Vc:FRV) of the FRVs implying that the conduit dominates ow trans-
port (Fig. 8b). These results are compatible with the natural karst water
systems that conduits are the main pathways of groundwater ow.
Furthermore, ~3 % (VL:FRV) of water volume is lost during the tests,
owing to the capillary action that retains capillary water at the interface
of the concrete block pores and the plexiglass box when the water level
in the ssure domain lowers. (Fig. 8b).
3.3. Simulation of solute storage and release processes
The DHDM was calibrated to simulate the BTCs quantitatively to
characterize the storage-release process generating anomalous trans-
port. The simulated results of the DHDM model display that the DHDM
robustly captured the skewness of long-tailing and bimodal character-
istics of the observed BTCs (Fig. 9). This is also conrmed quantitatively
by the higher NSE and lower RMSE computed, respectively. The best-
tted parameters of the DHDM for all tracer experiments are listed in
Table 3.
As the FRV increases from 9.0 to 32.5 L, the best-tted velocity of the
conduit domain (v1) increases from 1.10 to 1.40 m/s, which approxi-
mates the average velocity in conduit (v =1.25 ~ 1.40 m/s), whereas
the best-tted velocity of the ssure domain (v2) decreases from 0.90 to
0.13 m/s. The average ow velocity in the conduit and the ssures show
a negative relationship, with the conduit having a substantially higher
ow velocity than that of the ssures (Table 3).
As the FRV increases, the rst peak emerges earlier, whereas the
second peak emerges later. The bimodal structure of the BTCs becomes
more apparent with larger discrepancies in the velocity between
different domains. This implies that, when solute transport in both do-
mains is dominated by advection, a larger discrepancy or contrast be-
tween velocities can further separate the two concentration peaks. These
results conrm that the solute storage-release process is induced by
hydrodynamic conditions which agree with the results of Section 3.2.
The hydrodynamic dispersion coefcient in the conduit domain (D1)
is larger than in the ssure domain (D2), and is caused by the signicant
ow velocity in the conduit domain (Morales et al., 2010). Taken
collectively, the corresponding D1 did not change considerably and are
in the same order of magnitude. D2 decreases response to a reduction in
ow velocity in the ssure domain produced by an increase in retention
time. However, the parameters capturing time nonlocality (γ1 and γ2), as
well as the fractional capacity coefcient (β1) of conduit domain, remain
stable since the conduit-ssures structure remains maintained.
The ssure domains fractional volume coefcient (β2) drops from
0.27 to 0.08 indicating a relatively weaker impact of solute retention on
solute transport after a larger amount of recharge. The enhanced hy-
drodynamic conditions drive the volume of storage water in ssures,
giving further impetus to the total volume of ssure domain and
immobile zone to increase simultaneously. Nevertheless, the volume of
the immobile zone in the ssure domain increases at a slower rate as
compared to the total volume. Meanwhile, with the tracer injection
condition remaining the same, a larger φ2 means more solute being
trapped by the ssure domain, whereas the opposite is found for the
conduit domain (Table 3).
3.4. Quantitative analysis of solute in different ow paths
The DHDM simulation reveals that advection controls conservative
solute transport in the two domains. Combined with the analysis of the
solute storage-release processes in ssures, it shows that the total BTCs
are the superposition of the solute transport in the conduit and storage-
release paths. Therefore, the process of solute storage-release in ssures
could be considered as a relatively independent, slow transport
pathway.
Consequently, we utilized the best-tted parameters of Equation (1a)
(Table 3) to represent the solute transport process in the conduit. The
solute transport process in the storage-release path is obtained by sub-
tracting the conduit transport curve from the total BTCs. A quantitative
Fig. 9. Comparison between observed BTCs (symbols) and the simulated curves (red lines) obtained by DHDM simulation. The outlet discharge curves are blue lines;
I: the water storage stage; II: the recharge retention stage due to increased FRV; III: the ssures water release stage. (For interpretation of the references to colour in
this gure legend, the reader is referred to the web version of this article.)
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
9
estimate of the mass of solute transport in the conduit and storage-
release paths was conducted by integrating the product of the enve-
lope area of solute transport curves in the conduit and ssures with the
total injected mass (Fig. 10).
The results elucidated that the enhanced hydrodynamic conditions
initially push more solutes to be stored in ssures (Table 4), leading to
gradual decrease in solute transport mass in the conduit. As FRV in-
creases from 9.0 to 32.5 L, the solute storage mass (Ms) in the ssures
also increases from 8.3 to 11.5 g; simultaneously, the solute release mass
(Mr) increases from 7.5 to 8.5 g, while the solute transport mass (Mc) in
conduit decreases from 6.7 to 3.5 g (Fig. 11a). Accordingly, the pro-
portion of solute transport in the release path gradually increases from
50 % to 57 % (Mr:M) and decreases from 45 % to 23 % (Mc:M) in the
conduit as the FRV increases (Fig. 11b).
It should be noted that the solute recovery rates are approximately
80 % under higher hydrodynamic conditions (e.g., 32.5 L), and over 90
% under weaker hydrodynamic conditions (e.g., 9.0 L). As discussed
above, with the conduit-water entering the ssures, the volume of the
immobile zone in the ssure also increases, and the capillary action
retains and traps solute in the immobile zone, resulting in a partial loss
of solutes. Hence, the proportion of solute mass loss (ML) increases from
5 % to 20 % as the hydrodynamic conditions increase (Fig. 11).
It is shown that, due to the high ow velocity in the conduit, solutes
can be transported from the conduit to more distant ssure networks and
immobile zones for storage. Through this process, up to ~ 77 % of
solutes enter the ssure storage, ~20 % of solutes can be stored in the
system without being released, and this part of solutes may likely be
released in the next stronger focused recharge event (Table 4). That way,
the focused recharge may result in an underestimated and widespread
risk to usable groundwater volumes. Furthermore, when slow and
diffuse ows predominate during ssure release after focused recharge,
solutes can be released slowly and steadily into the conduit, thereby
maintaining a longer release time of solutes in karst aquifer.
3.5. Application and limitations of the laboratory analog
Karst groundwater is highly vulnerable owing to the focused
recharge through sinkholes. Due to the high speed and turbulent ows in
the conduit, solute transport is usually a transitory process (Vadillo and
Ojeda, 2022). However, rapid transport continues to be a major prob-
lem, as high concentrations of solutes could reach the system outlet
more rapidly without being able to foresee the event, which increases
the uncertainty about their movement due to the random distribution of
aquifer medium networks. This implies that the pollution risk of
groundwater is much larger than expected where focused recharge oc-
curs. Also, the slow release of storage solutes and pollutants, or even
ush out again by later recharge events, is a big challenge for ground-
water self-purication in karst aquifers. Consequently, the proposed
method for quantifying conservative solute mass may be helpful in
guiding karst groundwater pollution prevention, remediation, and
Table 3
The DHDMs best-tted parameters for BTCs from the solute transport experiments.
FRV (L) v1(m/s) v2(m/s) D1(m
2
/s) D2(m
2
/s) β1(sγ1) β2(sγ1) γ1(-) γ2(-) φ1(-) φ2(-)
9.0 1.10 0.90 2.30 1.40 0.05 0.27 0.7 0.7 0.30 0.70
11.0 1.10 0.60 2.25 1.50 0.05 0.27 0.7 0.7 0.40 0.60
13.0 1.15 0.45 1.40 0.60 0.05 0.23 0.7 0.7 0.33 0.67
19.5 1.20 0.28 1.65 0.40 0.05 0.20 0.7 0.7 0.26 0.74
26.0 1.40 0.20 1.50 0.20 0.05 0.16 0.7 0.7 0.24 0.76
32.5 1.40 0.13 1.40 0.15 0.05 0.08 0.7 0.7 0.23 0.77
Note: vi: the effective velocity in the i-th domain; Di: the hydrodynamic dispersion coefcient of the i-th domain; βi: the fractional capacity coefcient in the i-th
domain; γi: the time index representing the degree of time nonlocality for solute transport in the i-th domain; φi: the volume fraction of the i-th domain; i =1, 2.
Fig. 10. Comparison between observed BTCs (symbols) and the representative curve (red lines) of solute transport in conduit ow using Eq (1a). The solute transport
process in the storage-release path is green line. M
r: the solute mass of ssure release; MC: the solute mass of conduit transport. (For interpretation of the references to
colour in this gure legend, the reader is referred to the web version of this article.)
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
10
management.
The physical and laboratory-scale modeling of karst aquifers is an
effective approach to gain insights into the mechanisms controlling karst
groundwater ow and solute transport (Shu et al., 2020). Previous work
has used geometric, kinematic and mechanical similarities to scale up or
down site scale conditions to laboratory scale (Mohammadi et al.,
2021b). Notably, Scale effects are the main problems faced by
laboratory-scale physical models. The following limitations might occur
in the present work:(1) although the ow regime in the experiments is
turbulent, the Reynolds number can be greater in site scale tracer tests;
(2) due to scale effects, ow rates in site scale are typically much larger
than laboratory scale, which can affect tracer velocities and dispersive
DHDM transport parameters; (3) portraying the solute transport process
in dual media with variable ow rates and volume ratios is complex. In
subsequent studies, its worthwhile to develop more realistic models,
such as simulating solute transport processes in karst aquifers by
considering the spatial and temporal variation of ow velocities.
4. Summary and conclusion
This paper evaluated the inuences of focused recharge volumes
(FRVs) on the storage-release process and BTCs by performing experi-
mental instantaneous tracer tests through conduit and ssure systems. A
dual heterogeneous domain model (DHDM) was successfully calibrated
to simulate the transport process of conservative solute and quantita-
tively calculate the mass of the solute under focused recharge condi-
tions. The ndings and conclusions of this study are summarized as
follows:
(1) The magnitude of the focused recharge determines the strength of
the hydrodynamic conditions; the stronger the hydrodynamic
conditions, the greater the amount of water transported in the
conduit alone and the amount of water stored in the ssures, but
the proportions of both to the FRVs remain essentially constant.
(2) The hydrodynamic conditions strongly control the solute storage-
release process associated with anomalous transport and deter-
mine the solute retention time in the ssure domain. These con-
ditions produce strong asymmetry, long-tailing, or bi-peaks in the
BTCs. As hydrodynamic conditions increase, the BTCs shift from a
single peak to a bi-peak, and the separation of the rst and second
peaks become more apparent.
(3) The DHDM model can robustly capture the long-tailing in BTCs,
including the bimodal characteristics of the observed BTCs.
Specically, the ow velocity and dispersion coefcient are the
major variables that regulate the bimodal structure of the BTCs
and the solute storage-release differences between the conduit
and ssure domains. The bimodal structure of the BTCs becomes
more apparent for larger discrepancies in ow velocity.
(4) A method to quantify the solute mass in storage-release paths by
segmenting the solute transport curve in the conduit from the
total BTCs was proposed. Under strong hydrodynamic conditions,
the solute mass proportion of conduit transport was less than 23
%. In comparison, the solute mass proportion of ssure storage
was up to 77 % due to the large hydraulic gradients, but ~ 20 %
of solutes were stored in the system without being released dur-
ing the subsequent ssure release process.
These outcomes provide enhanced and improved insights into the
Table 4
Quantication and estimates of the solute transfer mass using Equation (1a).
FRV
(L)
MR(g) R
(%)
Ms(g) Mr(g) MC(g) ML(g) Ms:M(%) Mr:M(%) Mc:M(%) ML: M
(%)
9.0 14.2 95 8.3 7.5 6.7 0.8 55 50 45 5
11.0 13.6 91 9.2 7.8 5.8 1.4 62 52 38 9
13.0 12.9 86 10.0 7.9 5.0 2.1 67 52 33 14
19.5 12.5 83 11.0 8.5 4.0 2.5 73 56 27 17
26.0 12.4 82 11.2 8.5 3.9 2.7 74 57 26 18
32.5 12.0 80 11.5 8.5 3.5 3.0 77 57 23 20
Note: MR: the total recovery mass; R: the solute recovery rates; Ms: the solute mass of ssure storage; Mr: the solute mass of ssure release; Mc: the solute mass of
conduit transport; ML: the solute mass of loss.
Fig. 11. (a) Variations in solute mass transported via different paths with focused recharge. (b) The proportions of solute mass transported via different paths to the
total injected mass.
H. Ji et al.
Journal of Hydrology 612 (2022) 128228
11
impact of hydrodynamic conditions on storage and release of conser-
vative solute between karst conduit and ssures medium in karst
aquifer. Further, these ndings might be essential for better under-
standing solute transport in karst aquifers.
CRediT authorship contribution statement
Huaisong Ji: Conceptualization, Formal analysis, Methodology,
Software, Writing original draft, Visualization. Mingming Luo:
Conceptualization, Supervision, Project administration, Funding acqui-
sition, Resources, Writing review & editing. Maosheng Yin: Meth-
odology, Software, Writing review & editing. Chenggen Li: Data
curation, Visualization. Li Wan: Investigation, Visualization. Kun
Huang: Supervision, Writing review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
The authors are unable or have chosen not to specify which data has
been used.
Acknowledgments
This research was supported by the National Natural Science Foun-
dation of China (Grant No. 42172276, 41807199).
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