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A quantitative study on accumulation of age mass around stagnation points in nested flow systems

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The stagnant zones in nested flow systems have been assumed to be critical to accumulation of transported matter, such as metallic ions and hydrocarbons in drainage basins. However, little quantitative research has been devoted to prove this assumption. In this paper, the transport of age mass is used as an example to demonstrate that transported matter could accumulate around stagnation points. The spatial distribution of model age is analyzed in a series of drainage basins of different depths. We found that groundwater age has a local or regional maximum value around each stagnation point, which proves the accumulation of age mass. In basins where local, intermediate and regional flow systems are all well developed, the regional maximum groundwater age occurs at the regional stagnation point below the basin valley. This can be attributed to the long travel distances of regional flow systems as well as stagnancy of the water. However, when local flow systems dominate, the maximum groundwater age in the basin can be located around the local stagnation points due to stagnancy, which are far away from the basin valley. A case study is presented to illustrate groundwater flow and age in the Ordos Plateau, northwestern China. The accumulation of age mass around stagnation points is confirmed by tracer age determined by 14C dating in two boreholes and simulated age near local stagnation points under different dispersivities. The results will help shed light on the relationship between groundwater flow and distributions of groundwater age, hydrochemistry, mineral resources, and hydrocarbons in drainage basins.
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A quantitative study on accumulation of age mass around
stagnation points in nested flow systems
Xiao-Wei Jiang,
1,2
Li Wan,
1,2
Shemin Ge,
3
Guo-Liang Cao,
1,2
Guang-Cai Hou,
4
Fu-Sheng Hu,
1,2
Xu-Sheng Wang,
1,2
Hailong Li,
1,2
and Si-Hai Liang
1,2
Received 6 June 2012; revised 26 September 2012; accepted 26 September 2012; published 6 December 2012.
[1] The stagnant zones in nested flow systems have been assumed to be critical to
accumulation of transported matter, such as metallic ions and hydrocarbons in drainage
basins. However, little quantitative research has been devoted to prove this assumption.
In this paper, the transport of age mass is used as an example to demonstrate that
transported matter could accumulate around stagnation points. The spatial distribution of
model age is analyzed in a series of drainage basins of different depths. We found that
groundwater age has a local or regional maximum value around each stagnation point,
which proves the accumulation of age mass. In basins where local, intermediate and
regional flow systems are all well developed, the regional maximum groundwater age
occurs at the regional stagnation point below the basin valley. This can be attributed to the
long travel distances of regional flow systems as well as stagnancy of the water. However,
when local flow systems dominate, the maximum groundwater age in the basin can be
located around the local stagnation points due to stagnancy, which are far away from the
basin valley. A case study is presented to illustrate groundwater flow and age in the Ordos
Plateau, northwestern China. The accumulation of age mass around stagnation points is
confirmed by tracer age determined by
14
C dating in two boreholes and simulated age near
local stagnation points under different dispersivities. The results will help shed light on the
relationship between groundwater flow and distributions of groundwater age,
hydrochemistry, mineral resources, and hydrocarbons in drainage basins.
Citation: Jiang, X.-W., L. Wan, S. Ge, G.-L. Cao, G.-C. Hou, F.-S. Hu, X.-S. Wang, H. Li, and S.-H. Liang (2012), A quantitative
study on accumulation of age mass around stagnation points in nested flow systems, Water Resour. Res., 48, W12502, doi:10.1029/
2012WR012509.
1. Introduction
[2] Periodic undulations of the water table create gravity-
driven, hierarchically nested flow systems, i.e., local, inter-
mediate and regional flow systems in drainage basins
[To
´
th, 1963]. Even in homogeneous and isotropic basins,
the distribution of groundwater velocity in such nested flow
systems is extremely heterogeneous and stagnant zones
with low velocity could develop due to convergence and/or
divergence of groundwater flow systems. Mathematically,
stagnant zones are associated with stagnation points. The
dynamics of groundwater around stagnation points has been
studied numerically by Anderson and Munter [1981],
Winter [1976, 1978, 1999] and Winter and Pfannkuch
[1984] in studies on surface water-groundwater interaction.
The stagnation points had also been found to be useful in
defining capture zones [e.g., Tosco et al., 2008]. Based on
analytical solutions of hydraulic head and stream function,
Jiang et al. [2011] studied the dynamics of groundwater
around stagnation points in nested flow systems and found
that stagnation points could be divided into three types. A
regional convergent stagnation point, which is caused by
convergence of two flow systems, is located at the basin
bottom (Figure 1a); a regional divergent stagnation point,
which is caused by divergence of two flow systems, is also
located at the basin bottom (Figure 1b); a local stagnation
point, is located inside the basin and is caused by diver-
gence and convergence of four flow systems (Figure 1c).
‘Local’ is due to the fact that at least one of these four flow
systems belongs to a local flow system.
[
3] Based on qualitative analysis, To
´
th [1980, 1999] pro-
posed that transported matter such as metallic ions and
hydrocarbons could accumulate in stagnant zones. The accu-
mulation of metallic ions or petroleum in stagnant zones at
the discharge end of a basin where two regional flow systems
converge or a regional flow system ascends, i.e., around the
regional convergent stagnation points as shown in Figure 1a,
1
Key Laboratory of Groundwater Circulation and Evolution, China
University of Geosciences, Ministry of Education, Beijing, China.
2
School of Water Resources and Environment, China University of
Geosciences, Beijing, China.
3
Department of Geological Sciences, University of Colorado Boulder,
Boulder, Colorado, USA.
4
Xi’an Center of Geological Survey, China Geological Survey, Xi’an,
China.
Corresponding author: X.-W. Jiang, Key Laboratory of Groundwater
Circulation and Evolution, China University of Geosciences, Ministry of
Education, Beijing 100083, China. (jxw@cugb.edu.cn)
©2012. American Geophysical Union. All Rights Reserved.
0043-1397/12/2012WR012509
W12502 1of14
WATER RESOURCES RESEARCH, VOL. 48, W12502, doi:10.1029/2012WR012509, 2012
has been reported by several researchers [Baskov,1987;
Garven, 1985; Garven and Freeze, 1984; Sanford,1994;
To
´
th, 1980, 1988]. However, there has been little, if any,
quantitative research on the accumulation of transported mat-
ter in stagnant zones around regional divergent stagnation
points or local stagnation points. A quantitative understand-
ing on whether transported matter could accumulate around
stagnation points would allow direct application of the theory
of regional groundwater flow to explorations of mineral
resources and hydrocarbons.
[
4] The age of groundwater, as an intrinsic property of
groundwater, is an important factor in explaining the hydro-
chemistry and vegetation type on a regional scale [Batelaan
et al.,2003;Freeze and Cherry, 1979]. Groundwater age
can be calculated mathematically by solving the transport
equation or determined chemically by measuring tracers in
groundwater [Bethke and Johnson,2008;Phillips and
Castro, 2003]. In this paper, the former is called model age,
and the latter tracer age. Traditionally, model age is calcu-
lated using the piston-flow model. Goode [1996] defined the
concept of ‘age mass as the product of water mass and its
age. Groundwater age is an intensive quantity of ground-
water, which means that it is mass-independent and hence
not additive. Age mass, on the contrary, is an extensive
quantity which depends on the total mass of the system, and
is additive. Therefore, age mass can be considered as trans-
ported matter which could accumulate in groundwater. By
defining age mass, Goode [1996] developed the advection-
dispersion equation for age mass transport, which accounted
for the mixing of groundwater due to hydrodynamic disper-
sion. According to this definition, the age of a groundwater
sample is the average age of all the water molecules in the
sample for the length of time each molecule has spent in the
subsurface. This new age mass transport approach is chang-
ing the field of groundwater age dating [Bethke and Johnson,
2008]. By comparing the model age distribution of a cross-
section in the Carrizo aquifer calculated by three different
approaches, i.e., the piston-flow approach, the tracer trans-
port approach, and the age mass transport approach, Castro
and Goblet [2005] found that when groundwater velocity is
extremely heterogeneous within a single aquifer, the results
obtained by the age mass transport approach yield the most
consistent ages. Therefore, the age mass transport approach
is the most suitable method to obtain model age in nested
flow systems, whose velocity is extremely heterogeneous.
[
5] The emphasis of this study is to identify the charac-
teristics of age distribution around stagnation points where
transported matter is expected to accumulate. According to
To
´
th’s [1980, 1999] study, the low velocities in stagnant
zones are expected to result in old groundwater , i.e., accu-
mulation of age mass would lead to the existence of older
model ages around stagnation points and also older tracer
ages around stagnation points in a real basin. Note that
if the piston-flow model is employed, the age at a stagna-
tion point would be infinitely large, which is obviously
unrealistic.
[
6] In this paper, we first numerically obtain model age
distribution in a series of two-dimensional (2-D) synthetic
drainage basins using the classic To
´
th [1963] model and
discuss the characteristics of age distribution around stag-
nation points. We then use the Ordos Plateau as an example
to show the distributions of groundwater flow systems and
age around stagnation points.
2. Mathematical Models
[7] In studies on groundwater flow systems, it is usually
assumed that : (1) a 2-D cross-section of a basin is represen-
tative of a three-dimensional basin when it is taken parallel
to the direction of dip of the water table slope; and (2) the
average water table over many years is constant and can be
accepted as a specified head boundary [To
´
th, 1963; Freeze
and Witherspoon, 1967 ; Jiang et al., 2011]. Consequently,
we use the steady state groundwater flow equation to obtain
the flow field:
rðKrhÞ¼0; (1)
where K is the hydraulic conductivity tensor, h is the hy-
draulic head. The bottom of the basin is usually impervi-
ous. The two sides of the cross-section, which correspond
to the basin valley and the basin divide, are also considered
as no-flow boundaries.
Figure 1. Schematics defining three types of stagnation
points (SP): (a) A regional convergent SP formed by conver-
gence of two flow systems; (b) A regional divergent SP
formed by divergence of two flow systems; (c) A local SP
formed by convergence and divergence of four flow systems.
W12502 JIANG ET AL.: AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
2of14
[8] In this study, we only care whether age mass could
accumulate around stagnation points, so we calculate the
steady state model age. Steady state groundwater flow field
is used as input to obtain steady state age distribution. The
equation for steady state age mass transport is [Goode,
1996]
rðDr ÞrðuÞþ ¼ 0; (2)
where is the model age of groundwater , is effective po-
rosity, u is the pore velocity vector, D is the dispersion
coefficient tensor. For 2-D cross-section models, u ¼
[u
x
, u
z
], and D ¼
D
þ D
xx
D
þ D
xz
D
þ D
zx
D
þ D
zz

, where D
is the
molecular diffusion coefficient. To calculate each element
of D, we define u ¼ (u
x
2
þ u
z
2
)
1/2
, thus D
xx
¼
L
u
2
x
u
þ
T
u
2
z
u
,
D
xz
¼ D
zx
¼ð
L
T
Þ
u
x
u
z
u
, and D
zz
¼
L
u
2
z
u
þ
T
u
2
x
u
, where
L
and
T
are longitudinal and transverse dispersivities.
[
9] At the top boundary of the basin, recharge zones
obtained from flow simulation have zero age mass with
¼ 0, while discharge zones have zero dispersive age mass
flux with Dr ¼ 0. All other boundaries have zero age
mass flux with u Dr ¼ 0. The governing equations of
groundwater flow and age mass transport are solved using
the finite element method via COMSOL Multiphysics
[COMSOL AB, 2008; Li et al., 2009].
3. A Synthetic Study
[10] Distributions of chemistry and age of groundwater are
closely related to the velocity field. It is universally acknowl-
edged that heterogeneity of hydraulic conductivity would
greatly influence the distribution of velocity. In fact, the re-
gional topography-driven flow alone is enough to create
extremely heterogeneous velocity field. To exclude the influ-
ence of heterogeneity on the velocity field, we first use the
classic To
´
th [1963] model to examine the relationship
between stagnation points and groundwater age.
3.1. Basin Geometry and Parameters
[
11] The geometry of the cross-sections of drainage
basins is characterized by undulating water table on the top
boundary as we used in Jiang et al. [2009, 2010b]:
z
s
ðxÞ¼z
0
þ x tan þ
a
cos
sin
2x
cos

; (3)
where z
0
is the elevation of the valley bottom, is the angle
of the regional slope, a and are the amplitude and wave-
length of the local undulation of water table, and x is the
horizontal distance from the basin valley. We assume that
the basin bottom is flat and impervious.
[
12] For the geometry of the basin cross-section defined in
equation (3), we use z
0
¼ 1000 m, tan ¼ 0.02, a ¼ 15 m,
¼ 1500 m, and x ranges from 0 to 6000 m. We assume
that the drainage basin has a hydraulic conductivity of K ¼
1md
1
and a porosity of ¼ 0.3. In the calculation for
the elements of D, we assume the effective molecular diffu-
sion coefficient D
¼ 1.16 10
9
m
2
s
1
, the longitudinal
dispersivity
L
¼ 6 m, and the transverse dispersivity
T
¼ 0.6 m. The longitudinal dispersivity and transverse
dispersivity are assumed to be constant in space, which is
typical in studies on regional flow and transport modeling
[Zheng and Bennett, 2002].
3.2. Characteristics of Age Around Stagnation Points
[
13] When the basin depth at the basin valley is 1000 m,
three orders of flow systems, namely, local, intermediate and
regional flow systems are all well developed (Figure 2a).
There are one regional convergent stagnation point (SP 5),
one regional divergent stagnation point (SP 6) and four local
stagnation points (SP 1 through SP 4). Groundwater is
increasingly older from the recharge zone to the discharge
zone in each flow system. Near the end of an intermediate or
regional flow system, due to the differences in travel dis-
tance, there is an abrupt change in groundwater age from ba-
sin top to basin bottom, i.e., the color representing logarithm
of age changes from blue and yellow to red. To identify the
characteristics of groundwater age around the local stagna-
tion points, we show the distributions of groundwater age
and flow systems around two of the four local stagnation
points, SP 2 and SP 3 (Figure 3). Near each stagnation point,
there is a closed line of contour, indicating trap of age mass
around local stagnation points.
[
14] We also use some ‘boreholes’ penetrating stagna-
tion points to show the variations in groundwater age with
depth (Figure 4). For the four local stagnation points, SP 1
through SP 4, age profiles show that groundwater ages have
their local maximum values near stagnation points. For the
two regional stagnation points, SP 5 and SP 6, groundwater
ages have maximum values at the stagnation points. More-
over, groundwater at SP 5 is the oldest in the entire basin.
[
15] Based on the contours of groundwater age around
local stagnation points shown in Figure 3 and the maximum
values of groundwater age in the profiles shown in Figure 4,
we can conclude that older water can be found not only
around regional convergent stagnation points (SP 5), but
also around regional divergent stagnation points (SP 6) and
local stagnation points (SP 1 through SP 4), i.e., age mass
could accumulate around each type of stagnation points.
3.3. Effect of Depth of Local Stagnation Points on Age
Distribution
[
16] According to To
´
th [2009], the influencing factors of
flow pattern in basins can be grouped into water table con-
figuration, basin depth, heterogeneity and anisotropy . Jiang
et al. [2010b] studied the influence of depth-decaying hy-
draulic conductivity and porosity on model age in a unit ba-
sin and a To
´
th basin with the same basin depth. Here, we
use drainage basin s with different depths to discuss the
relationship between the distributions of groundwater flow
systems, depths of local stagnation points and groundwater
age. Deeper local stagnation points have been suggested in
settings where the amplitude of local undulation is high,
the amplitude of regional undulation is low, the hydraulic
conductivity decays rapidly with depth, or the anisotropy
ratio (the ratio of horizontal hydraulic condu ctivity to verti-
cal hydraulic conductivity) is small [Jiang et al., 2011;
To
´
th, 1963; Wang et al., 2011]. Therefore, although only
the effect of basin depth is considered, the results of this
study can be applied to other situations. For example, the
flow pattern in a homogeneous basin with a large depth is
W12502 JIANG ET AL. : AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
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similar to the flow pattern in a homogeneous basin with a
small depth and a large anisotropy ratio.
[
17] The distributions of groundwater flow systems, stag-
nation points, and model age for basins with different
depths are shown in Figure 2. As the basin depth decreases,
there is less room for intermediate and regional flow sys-
tems to develop, and the local stagnation points might
reach the basin bottom. When the basin depth reduces to
500 m, SP 1 reaches the basin bottom and splits into two
new stagnation points (SP 1 caused by convergence of two
flow systems and SP 1
0
caused by divergence of two flow
systems as shown in Figure 2c). In this case, the regional
flow cannot reach the basin valley. When the basin depth
reduces to 400 m, SP 4 also reaches the basin bottom and
splits into two new stagnation points (SP 4 and SP 4
0
as
shown in Figure 2e). In this case, groundwater recharged at
the divide can only discharge locally.
[
18] Accompanying with the changes in relative depths
of local stagnation points, the location of maximum age in
the basins, where transported matter is most likely to accu-
mulate, also changes, although remains to happen at the ba-
sin bottom. When local, intermediate and regional flow
systems are well developed (Cases a and b in Figure 2), the
stagnation point below the basin valley (SP 5) has the max-
imum age. In Case c, when SP 1 reaches the basin bottom,
groundwater at the new SP 1 (convergence) has the
maximum age. When the basin depth reduces from 500 m
(Case c) to 450 m (Case d), although the development of
flow systems differs little (SP 4 does not reach basin bot-
tom yet), the location of maximum age shifts from SP 1 to
the basin bottom below SP 4. When the basin depth reduces
to 400 m (Case e), SP 4 reaches the basin bottom, and
groundwater at the new SP 4 (convergence) has the maxi-
mum age. We can infer that old groundwater could exist
not only near the basin valley, but also other parts of a ba-
sin below the topographic lows where stagnation points
exist. In other words, a long travel distance is not the only
factor producing maximum groundwater age, and stagnancy
within short travel distance could also result in maximum
groundwater age. This finding is valuable for interpreting
groundwater age distribution, groundwater chemistry and
potential sites of concentrating minerals or petroleum.
4. A Field Study in the Ordos Plateau
[19] Groundwater age can be determined chemically by
the concentration of tracers. A combination of tracer age
and model age would be convincing to prove the accumula-
tion of age mass around stagnation points. Here, we use a
cross-section in the Ordos Plateau as a typical site to exam-
ine the relationship between groundwater flow systems,
stagnation points and age distribution.
[
20] The Ordos Basin, the second largest sedimentary basin
in northwestern China, is abundant in fossil fuel and mineral
resources. Unfortunately, the economic development of the
Ordos Basin is restricted by limited water resources due to its
Figure 2. The distributions of groundwater flow systems, stagnation points and groundwater age
in synthetic drainage basins with different basin depths (Z). Solid lines are pathlines. (a) Z ¼ 1000 m;
(b) Z ¼ 550 m; (c) Z ¼ 500 m; (d) Z ¼ 450 m; (e) Z ¼ 400 m.
W12502 JIANG ET AL.: AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
4of14
arid to semiarid climate. Since 1999, a project ‘Groundwater
Investigation in the Ordos Basin’ was launched by the China
Geological Survey [Hou et al., 2008a]. Results of this project
indicate that groundwater flow is topographically controlled
in the northern part of the Ordos Basin, which is also called
the Ordos Plateau [Hou et al., 2008b]. Moreover, stable iso-
tope analysis shows that groundwater in the Ordos Plateau is
of meteoric origin [Yin et al., 2010; Yin et al., 2011].
4.1. An Overview of the Study Area
[
21] The Ordos Plateau extends 360 km from north to
south while about 210 260 km from west to east, cover-
ing an area of 81,000 km
2
. Precipitation and evaporation
are unevenly distributed in the study area (Figure 5). Pre-
cipitation decreases from 420 mm yr
1
in the southeast to
160 mm yr
1
in the northwest. The potential evaporation is
Figure 3. Distributions of groundwater flow systems and age around local stagnation points. (a) SP 2;
(b) SP 3. (The black lines are contours of groundwater age, the red lines are pathlines, and the arrows
represent flow direction.)
W12502 JIANG ET AL. : AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
5of14
extremely high, increasing from 2000 mm yr
1
in the
southeast to 3200 mm yr
1
in the northwest. Precipitation
mostly occurs as rainfall from July to September. The
mean monthly temperature can be as high as 20.7
C in July
but as low as 4.6
C in January, with a mean annual tem-
perature of 6.5
C[Yin et al., 2010 ; Yin et al., 2011].
[
22] The Plateau has an undulating topography. The
major basin divides are the Baiyu Mountain at the southern
margin, with elevations ranging from 1500 to 1800 m, and
the Sishi Ridge, which strikes roughly northeast, with ele-
vations of 1400 1500 m (Figur e 5). The eastern, western
and northern margins, at elevations of 1100 1200 m, con-
stitute the basin valleys. There are numerous local topo-
graphic lows and highs. As a result of groundwater discharge
as well as surface runoff, lakes develop in some local lows.
There are three major rivers in the area: the Molin River, the
Dosit River and the Wuding River (Figure 5), all of which
are supplied mainly by groundwater.
Figure 4. Vertical profiles of groundwater age through (a) Local stagnation points, and (b) Regional
stagnation points, for the case shown in Figure 2a.
Figure 5. The location of the study area and the spatial distributions of precipitation and evaporation
in the Ordos Plateau (modified from Yin et al. [2011]).
W12502 JIANG ET AL.: AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
6of14
[23] In the Ordos Plateau, the basement consists of sand-
stones of Jurassic age (J), wh ich is low in porosity and per-
meability. Overlying the basement is the major sandstone
aquifer system of Cretaceous age, which comprises three
groups: in ascending order, the Luohe Group (K
1
l), the
Huanhe Group (K
1
h), and the Luohandong Group (K
1
lh).
The Cretaceous sandstones, which are poorly consolidated,
can be considered as a continuum type of porous medium.
The sandstone aquifer system is overlain locally by Terti-
ary (E) mudstones and extensively by unconsolidated Qua-
ternary (Q) sediments.
4.2. Geological and Hydrogeological Setting of the
Typical Cross-Section
[
24] Based on the equipotential map of the Ordos pla-
teau, we selected a 2-D cross-section (A-A
0
in Figure 5) for
analysis of groundwater flow. The cross-section is gener-
ally parallel to the direction of groundwater flow with some
adjustment to include as many research boreholes as possi-
ble. It spans about 240 km and has elevations ranging
between 1200 and 1450 m. The Sishi Ridge at the middle
of the cross-section has the highest elevation and is the
main recharge area.
[
25] Figure 6 shows the stratigraphy and lithology of the
cross-section. The basement geometry shows that the basin
is an asymmetric syncline. At the core of the syncline, near
borehole B2, the sandstone aquifer system has its maxi-
mum thickness of 950 m. The main sandstone aquifer sys-
tem thins eastward and pinches out at the end of the basin.
[
26] The aquifer system of the cross-section consists
mainly of K
1
h and K
1
l sandstones. The K
1
h sandstone was
deposited in a fluvial environment. The eastern part of the
K
1
l sandstone was deposited in an eolian environment
while the western part was deposited in a fluvial environ-
ment. There are numerous sporadic clay lenses in the K
1
h
and K
1
l sandstones. In the west end of the cross-section,
the K
1
lh sandstone and Tertiary mudstones are locally dis-
tributed. Most part of the cross-section is overlain by thin
Quaternary sediments.
[
27] The K
1
l sandstone, with a thickness of about 200 m,
is one of the two most important aquifers. Based on poros-
ity measurements of rock samples from boreholes B2 and
B7 (Figure 6), the mean porosity of fluvial sandstone is
21.1%. Eolian sandstone rock samples from borehole B15
were measured to have a mean porosity of 27.8%. There-
fore, the porosity of the eolian sandstone differs greatly
from that of the fluvial sandstone.
[
28]TheK
1
h sandstone is the other major aquifer. Its
thickness reaches 750 m at the core of the syncline near B2.
At the western edge, the thickness of K
1
h sandstone
decreases to 600 m. At borehole B15, its thickness decreases
to 260 m. At the eastern edge, the K
1
h sandstone finally
pinches out. Based on porosity measurements of rock sam-
ples from B2, B7 and B15, the porosity of fluvial sandstone
ranges between 16.5% and 24.5%.
[
29] In borehole B2, pumping tests were conducted at
three different depths using single well pumping tests. The
results of pumping tests give hydraulic conductivity values
of 0.38 m d
1
of the upper section of K
1
h sandstone and
0.18 m d
1
of the lower section of K
1
h sandstone. In con-
trast, the hydraulic conductivity of the K
1
l sandstone is
0.45 m d
1
. This indicates that K
1
l sandstone has a larger
hydraulic conductivity than K
1
h sandstone, and inside the
K
1
h sandstone, the deep part has a smaller hydraulic conduc-
tivity than the shallow part. This implies a depth-dependent
hydraulic conductivity structure in the K
1
h sandstone.
[
30] To examine the hydraulic conductivity structure of
whole aquifer system, we use 170 hydraulic conductivity
measurements in the K
1
h sandstone and 70 data in the K
1
l
sandstone throughout the Ordos Plateau. These hydraulic
conductivity values are obtained on the basis of pumping
test at many wells, whose depths of test sections are differ-
ent. Statistical analysis shows that hydraulic conductivity
of the K
1
l sandstone has no significant correlation with
depth, while mean hydraulic conductivity of the K
1
h sand-
stone decreases with depth (Figure 7). We use the exponen-
tial decay model [Jiang et al., 2010a; Jiang et al., 2009] to
fit the relationship between mean hydraulic conductivity and
depth. The decay exponent, A, is found to be 0.0022 m
1
(Figure 7).
[
31] There is a permeable fault near the western end of
the cross-section. West of the fault are formations of Juras-
sic and older age that constitute an impervious boundary of
the aquifer system. The Hekou Reservoir near the eastern
Figure 6. The geological cross-section of A-A
0
.
W12502 JIANG ET AL. : AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
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end is the lowest discharge zone in the eastern part of the
aquifer system, representing a no-flow boundary beneath
the Hekou Reservoir. On the basis of water level, hydro-
geochemistry and isotope data, it has been shown that
groundwater flow is topographically controlled with three
orders of flow systems (Figure 8) [Hou et al., 2008b; Yin
et al., 2010; Yin et al., 2011]. Groundwater recharged
around the Sishi Ridge could discharge locally via local
flow systems, to the Dosit River via an intermediate flow
system, and to the west end and the Hekou Reservoir near
the east end via regional flow systems.
4.3. Numerical Model
[
32] In analyses of groundwater flow systems, available
data are often insufficient to accurately determine the ele-
vation of water table. It is, therefore, customary to assume
that the long-term average water table over years conforms
to the topography and groundwater flow is in steady state
[Ophori and To
´
th, 1989; Sykes et al., 2009 ; To
´
th, 1963].
The 2-D steady state flow assumption has also been com-
monly used in regional-scale groundwater flow and trans-
port studies such as Bethke et al. [1999], Castro et al.
[1998], Castro and Goblet [2003]. Because of limited histor-
ical data, we assume that groundwater flow is in steady state
in our study area. The steady state groundwater flow assump-
tion is an acceptable first step toward a quantitative under-
standing of stagnation zone development in the study area.
[
33] A numerical model of steady state groundwater flow
and age of the cross-section is developed. The model area
is bounded by the water table on the top, the top of Jurassic
sandstone at the bottom, the boundary between the fault
and Jurassic and older formations at the west, and a water
divide at the east (Figure 9). This implies that only satu-
rated groundwater flow is considered. In the current study
area, although the climate is semiarid, due to the differen-
ces in hydraulic conductivity between the Cretaceous sand-
stones and the Quaternary sediments, groundwater exists in
the Quaternary sediments and the water table lies over the
top of the Cretaceous sandstones. For the most part of the
cross-section where the Quaternary sediments are thin, we
use the top of the Cretaceous sandstones to represent the
water table. For the east part where Quaternary sediments
are thick, we use interpolation to obtain the water table
based on limited water table measurements.
[
34] The model area includes five hydrostratigraphic
units: the fault, the K
1
l fluvial sandstone, the K
1
l eolian
sandstone, the K
1
h fluvial sandstone, and the Quaternary
Figure 8. The conceptual model of groundwater flow in cross-section A-A
0
(modified from Hou et al.
[2008b], with permission of Wiley).
Figure 7. The change in mean hydraulic conductivity
with depth in the K
1
h sandstone.
W12502 JIANG ET AL.: AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
8of14
sediments (Figure 9). Note that the small K
1
lh sandstone
and Tertiary mudstones near the western end of the cross-
section, are lumped into the K
1
h fluvial sandstone.
[
35] The 2-D steady state groundwater flow equation and
steady state age mass transport equation are solved using
the finite element method via COMSOL Multiphysics. The
model area is discretized into triangles, with a maximum
element size of 20 m. The mesh has 899,340 nodes, and
1,771,770 elements. For the groundwater flow model, the
top boundary has specified heads and three other bounda-
ries are impervious (Figure 9). For the age mass transport
model, the no-flow boundaries for groundwater flow have
zero age mass flux, the recharge zones on the specified
head boundary have zero age mass, and the discharge zones
on the specified head boundary have zero dispersive age
mass flux.
[
36] Porosity, hydraulic conductivity and dispersivity are
primary input parameters for groundwater flow and age
mass transport modeling. Porosity is mainly determined by
porosity measurements of rock samples from B2, B7, and
B15 and the ratio of sandst ones to clays in the sandstone
aquifer system. The distribution of porosity follows the di-
vision of the model area shown in Figure 9. When the clays
are considered, the porosity of K
1
h fluvial sandstone, K
1
l
fluvial sandstone and K
1
l eolian sandstone is 19.3%,
18.9%, and 27.8%, respectively. No measurements of po-
rosity of the fault and the Quaternary sediments are avail-
able. The porosity of the fault is assum ed to be larger than
that of the K
1
h fluvial sandstone and K
1
l fluvial sandstone,
while the porosity of the Quaternary sediments is assumed
to be larger than that of the K
1
l eolian sandstone. The po-
rosity of the fault and the Quaternary sediments is set to be
25% and 30%. Due to their small area compared with the
Cretaceous sandstones, we believe that this uncertainty would
not have a significant influence on the simulation results.
[
37] For large-scale models, sandstones with clays can
be characterized as an anisotropic medium, whose horizon-
tal hydraulic conductivity (K
x
) is mainly determined by the
sandstones and the vertical hydraulic conductivity (K
z
)by
the clays. Although in situ measurements of transmissivity
are available, they cannot be directly applied in the numeri-
cal model due to the existence of clays, which impose
uncertainties on the effective thickness of the aquifer, thu s
the calculation of K
x
. Here, the values of K
x
and anisotropy
ratio (K
x
/K
z
) are inversely determined. The value of K
x
/K
z
is assumed to be constant within each hydrostratigraphic
unit. In the hydrostratigraphic unit of K
1
h sandstone, the
depth-decaying hydraulic conductivity shown in Figure 7 is
also applied.
[
38] Defining dispersivity values for field-scale transport
simulation is inherently difficult and controversial [ Zheng
and Bennett, 2002]. In Castro and Goblet’s [2005] study
on age mass transport and
14
C transport models, the longi-
tudinal dispersivity was assumed to be 125 m, which is
around 1/1000 of the distance from the recharge zone to the
discharge zone in the cross-section. In our cross-section,
the distance from the divide to the basin valleys is around
100 km, so we assume the longitudinal dispersivity to be
100 m and the transverse dispersivity to be 10 m for cali-
bration of the model. Sensitivity analysis of dispersivity on
age distribution had also been conducted.
[
39] The information used for model calibration includes
the conceptual model of groundwater flow shown in Figure 8,
the hydraulic head measured at different depths of B15 by
packer test, and the isotopic age of
14
C in the K
1
l sandstone
part of B2 and B7. After model calibration by the trial and
error method, the horizontal hydraulic conductivity, K
x
,of
K
1
l fluvial sandstone is found to be 1.4 m d
1
,ofK
1
l eolian
sandstone is found to be 2.1 m d
1
. The initial K
x
(horizon-
tal hydraulic conductivity at or near ground surface) of K
1
h
fluvial sandstone was determined at 0.8 m d
1
. The values
of K
x
/K
z
of K
1
l fluvial sandstone, K
1
l eolian sandstone, and
K
1
h fluvial sandstone are 700, 600 and 520, respectively.
These anisotropy ratio values are in agreement with
Bethke’s [1989] and Deming’s [2002] findings that anisot-
ropy ratio could be of the order of 10
2
to 10
3
in large sedi-
mentary basins. The selections of hydraulic conductivity
and anisotropy ratio of the Quaternary sediments and fault
are more arbitrary due to limited information available and
their small area. Because they are more permeable than the
Figure 9. The hydrostratigraphy of the model area and boundary conditions for groundwater flow.
W12502 JIANG ET AL. : AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
9of14
sandstone aquifer system, the K
x
of Quaternary sediments
is set to be 10 m d
1
and that of the fault is set to be
4md
1
. Because they are relatively unconsolidated, the
K
x
/K
z
of Quaternary sediments and fault are set to be 50
and 100, respectively.
[
40] The measured hydraulic head by packer test and the
simulated hydraulic head at different depths of B15 are
shown in Figure 10. The absolute values of the differences
between measured and simulated hydraulic head range
between 0.20 m and 1.51 m, demonstrating that the hetero-
geneity and anisotropy of hydraulic conductivity is well
characterized. During calibration, we found that the rate of
decrease in hydraulic head with depth in the K
1
h sandstone
is sensitive to the anisotropy ratio, suggesting that the hy-
draulic head measured at different depths of a borehole
could be useful in estimating this parameter.
[
41] Groundwater were sampled at different parts of
boreholes B2 and B7, which were screened at different
depths. The
14
C ages, which were measured by the IAEA
using the method of liquid scintillation counting, in the K
1
l
sandstone part of B2 and B7 were used for model calibra-
tion. According to the conceptual model of groundwater
flow shown in Figure 8, groundwater mainly flows horizon-
tally in the K
1
l sandstone part of B2, and is near a regional
divergent stagnation point in the K
1
l sandstone part of B7.
The
14
C ages in the K
1
l sandstone part of B2 and B7 are
21,400 years and 19,110 years, respectively (Figure 11c).
The simulated age in the K
1
l sandstone part of B2 is around
21,500 year, and is very close to the measured age. B7 is
located near the divide, where a stagnation point exists at the
bottom. The simulated age around the stagnation point, SP 3,
which is about 19,000 24,000 years, is also in agreement
with the measured age in the K
1
l sandstone, which equals
19,110 years.
[
42] Groundwater sampled from the K
1
h sandstone part
of B7 was measured to be 440 years (Figure 11c), however,
the simulated age ranges between 0 and 9000 years from
the top to the bottom of the K
1
h sandstone. It is hard to
compare these two values because it is difficult to tell
which depth groundwater had been sampled at. In B15, the
measured age of groundwater sampled at eight different
depths has a narrow variation ran ging between 1450 years
and 2240 years, while the simulated age at corresponding
depths increases nonlinearly from 2000 years to 4000
years.
4.4. Simulation Results
[
43] The distributions of hydraulic head, groundwater flow
systems and groundwater age of the cross-section obtained
from the calibrated model are shown in Figure 11. Hydraulic
head is high around the Sishi Ridge, and has a general trend
of decreasing toward west and east (Figure 11a). Around the
Sishi Ridge, which is the regional recharge zone, hydraulic
head ranges between 1370 and 1380 m. In the middle of the
Sishi Ridge and the Hekou Reservoir, there is a zone with
hydraulic head larger than 1370 m. This local high consti-
tutes a local recharge zone. To the west of the Dosit River,
there is also a local recharge zone, with hydraulic head larger
than 1230 m.
[
44] At the recharge zones, for example, around the Sishi
Ridge, the shallow part of the aquifer system has a higher
hydraulic head than the deep part. This indicates that
groundwater mainly flows downward. At the discharge
zones, for example, around the Dosit River, the shallow part
of the aquifer system has a lower hydraulic head than the
deep part, which indicates that groundwater flows upward.
In the zone between the Sishi Ridge and the Dosit River, the
contours of hydraulic head are almost vertical, which implies
that horizontal flow dominates.
[
45] As discussed by Anderson and Munter [1981], To
´
th
[1988], and Jiang et al. [2011], groundwater around stagna-
tion points has the characteristics of potentiometric mini-
mum. Based on the shape of contours of hydraulic head
near the Dosit River, we can infer that there is a stagnation
point below this zone.
[
46] Streamlines help to identify the flowpath of ground-
water and the distribution of groundwater flow systems
(Figure 11b). The Sishi Ridge is the recharge zone of two
regional flow systems, one intermediate flow system and
one local flow system. Figure 11b also shows the location
of two local stagnation points (SP 1 and SP 2) and one re-
gional divergent stagnation points (SP 3). SP 1 west of the
Dosit River divides four flow systems, including two local
flow systems, one intermediate flow system and one re-
gional flow system. SP 2 east of the Sishi Ridge also
divides four flow systems, including three local flow sys-
tems and one regional flow system. Moreover, due to the
differences in basin depth, the locations of the two stagna-
tion points differ greatly, with SP 1 around the middle and
SP 2 near the bottom of the aquifer system. SP 3 below the
Sishi Ridge divides two regional flow systems.
[
47] Due to factors as basin geometry (varying basin
thickness) as well as heterogeneities and anisotropy of the
medium, the distribution of the groundwater age pattern is
more complex in the study area than that in the theoretical
cases shown in Figure 2. West of the Sishi Ridge, local
flow systems form in the shallow parts of the aquifer sys-
tem, and intermediate and regional flow systems develop in
the deep parts. Consequently, groundwater is generally older
in the deep part than at shallow depths. Near the western end
of the aquifer system, i.e., the ascending limb of regional
flow system, groundwater can be as old as exceeding 40,000
years. At the ascending limb of intermediate flow system
Figure 10. The measured and simulated hydraulic head
at different depths of B15.
W12502 JIANG ET AL.: AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
10 of 14
near the Dosit River, groundwater can be as old as around
20,000 years.
[
48] East of the Sishi Ridge, the Hekou Reservoir is the
lowest discharge region. Although groundwater can reach
the Hekou Reservoir through a regional flow system, local
flow systems dominate. Due to the large penetration depths
of the two local flow systems over SP 2 in Figure 11b,
groundwater has its maximum age (larger than 60,000
years but smaller than 120,000 years) around SP 2. This
phenomenon is similar to the age distribution around SP 4 in
Figure 2c. Sensitivity analysis of dispersivity shows that,
smaller dispersivity would lead to an even greater maximum
Figure 11. The distributions of hydraulic head, groundwater flow systems and age: (a) The contours of
hydraulic head; (b) streamlines showing local (green lines), intermediate (red lines) and regional (blue
lines) groundwater flow systems; (c) The distributions of groundwater age (gray lines are contour, red
lines represent boreholes, and black dots on the boreholes represent age measurements).
W12502 JIANG ET AL. : AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
11 of 14
age, while larger dispersivity would result in much younger
waters.
4.5. Discussions
[
49] The characteristics of dynamics and age of ground-
water around the local stagnation point SP 1 in Figure 11b
are discussed below. This point is chosen because borehole
B2, where measurements of
14
C age are available, might be
within the zone of influence of SP 1. Figure 12 shows the
distributions of groundwater age in the western part of the
cross-section, as well as four contours of hydraulic head,
two dividing streamlines and four schematic streamlines
showing the flow direction. The four contours of hydraulic
head of 1220.51 m and 1220.55 m, show the potentiometric
minimum around SP 1. The two dividing streamlines pre-
cisely divide the four flow systems.
[
50] In Figure 12, it is evident that groundwater below
SP 1 is much older than groundwater above SP 1. We plot
the vertical distribution of groundwater age through SP 1
under different dispersivities (Figure 13a). Under different
longitudinal dispersivities ranging between 30 and 300 m,
groundwater age has an abrupt increase near SP 1, and
reaches a maximum value below SP 1. Beyond the zone of
influence of the stagnation point, due to the heterogeneity
caused by lithology difference between K
1
h and K
1
l,
groundwater age decreases to a certain value.
[
51] In B2, the
14
C age in the lower part of K
1
h sand-
stone is measured to be 26,060 years, which is several thou-
sands years older than groundwater in the K
1
l sandstone
(21,400 years). In our calibrated model (
L
¼ 100 m), the
maximum age in the lower part of K
1
h sandstone is about
24,260 years, which is almost 3000 years older than the
simulated age in the K
1
l sandstone (Figure 13b). If a
smaller dispersivity
L
¼ 30 m is used, the maximum age
in the lower part of K
1
h sandstone is about 7000 years older
than the simulated age in the K
1
l sandstone. If a larger dis-
persivity
L
¼ 300 m is used, the maximum age in the
lower part of K
1
h sandstone is still about 2000 years older
than the simulated age in the K
1
l sandstone.
[
52] Here, both tracer age and model age under different
dispersivities demonstrate that within the zone of influence
of a stagnation point, groundwater age can be higher than
surrounding areas, i.e., age mass could accumulate in stag-
nant zones around local stagnation points. If an extremely
large dispersivity is used, however, it is possible that accu-
mulation of age mass might be negligible due to the high
degree of mixing.
[
53] The age data in the study area are limited at this
stage, but available data support the model results. In the
three available deep wells with age measurements, we
found that two of them are located near stagnation points,
i.e., B2 is located near a local stagnation point and B7 is
located near a regional divergent stagnation point below the
divide. Future efforts could be directed to collecting more
age data in the area around the Dosit River (Figure 11c) at
the elevation of 700800 m.
5. Conclusions
[54] We analyzed groundwater flow systems and ground-
water age in cross-sections of drainage basins of varying
depth. The characteristics of groundwater age around stagna-
tion points are emphasized. We find that age mass can accu-
mulate around stagnation points. In basin s where local,
intermediate and regional flow systems are all well developed,
Figure 12. Dynamics and age of groundwater around SP 1 (the gray lines around the SP are contours
of hydraulic head and the red lines are dividing streamlines).
W12502 JIANG ET AL.: AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
12 of 14
the maximum groundwater age is located at the stagnation
point below basin valley. When regional flow is weak or
absent, local stagnation points can be close enough to, or even
reach, the basin bottom. In such cases maximum groundwater
age can be located around local stagnation points, which are
far away from the basin valley. Consequently, maximum
groundwater age can be caused not only by long travel distan-
ces combined with stagnancy, but also by stagnancy with a
short travel distance.
[
55] A cross-section model of steady state groundwater
flow and age in the Ordos Plateau was constructed. The
model is calibrated using hydraulic head measurements
from different depths of one borehole and tracer ages meas-
ured in the K
1
l sandstone of two boreholes. Due to the dif-
ference in basin depth, groundwater flow patterns west and
east of the Sishi Ridge differs greatly. A relatively shallow
sub-basin east of the Sishi Ridge results in dominantly local
flow systems, while a relatively deep sub-basin west of the
Sishi Ridge leads to well developed local, intermediate and
regional flow systems. The measured
14
C age in borehole B2
and the model age at SP 1 and nearby areas under different
dispersivities demonstrate that within their zones of influence,
age mass could accumulate around local stagnation points.
[
56] The results reported in this study are fundamental to
the future applicability of the theory of regional ground-
water flow, such as interpreting tracer age and hydrochemi-
cal patterns, and exploration of mineral deposits or
petroleum. In the future, more field work is needed to fur-
ther demonstrate the accumulation of transported matter due
to stagnancy of groundwater and to obtain basin-scale val-
ues for dispersivity.
[57] Acknowledgments. This study was supported by China Geologi-
cal Survey (grant 1212011121145), National Natural Science Foundation
of China (grant 41202173), and the Fundamental Research Funds for the
Central Universities of China. The authors acknowledge three anonymous
reviewers and Jo´zsef To´th as a reviewer for their valuable comments that
have significantly enhanced the quality of this manuscript. The authors
also thank Associate Editor, Daniel Ferna`ndez-Garcia, and Editor, Graham
Sander, for their constructive suggestions.
References
Anderson, M. P., and J. A. Munter (1981), Seasonal reversals of ground-
water flow around lakes and the relevance to stagnation points and lake
budget, Water Resour. Res., 17, 1139–1150, doi:10.1029/WR017i004
p01139.
Baskov, E. A. (1987), The Fundamentals of Paleohydrogeology of Ore
Deposits, Springer, Berlin.
Batelaan, O., F. De Smedt, and L. Triest (2003), Regional groundwater
discharge: Phreatophyte mapping, groundwater modelling and impact
analysis of land-use change, J. Hydrol., 275(1), 86–108, doi:10.1016/
S0022-1694(03)00018-0.
Bethke, C. M. (1989), Modeling subsurface flow in sedimentary basins,
Geol. Rundsch., 78(1), 129–154, doi :10.1007/BF01988357.
Bethke, C. M., and T. M. Johnson (2008), Groundwater age and groundwater
age dating, Annu. Rev. Earth Planet. Sci., 36, 121152, doi:10.1146/
annurev.earth.36.031207.124210.
Bethke, C. M., X. Zhao, and T. Torgersen (1999), Groundwater flow and
the
4
He distribution in the Great Artesian Basin of Australia, J. Geophys.
Res., 104(B6), 12,999–13,011, doi:10.1029/1999JB900085.
Castro, M. C., and P. Goblet (2003), Calibration of regional groundwater
flow models: Working toward a better understanding of site-specific sys-
tems, Water Resour. Res., 39(6), 1172, doi:10.1029/2002WR001653.
Castro, M. C., and P. Goblet (2005), Calculation of ground water ages—A
comparative analysis, Ground Water, 43, 368–380, doi:10.1111/j.1745-
6584.2005.0046.x.
Castro, M. C., P. Goblet, E. Ledoux, S. Violette, and G. de Marsily (1998),
Noble gases as natural tracers of water circulation in the Paris Basin:
2. Calibration of a groundwater flow model using noble gas isotope data,
Water Resour. Res., 34(10), 2467–2483, doi:10.1029/98wr01957.
COMSOL AB (2008), COMSOL Multiphysics User’s Guide, COMSOL
AB, Stockholm.
Deming, D. (2002), Introduction to Hydrogeology, McGraw-Hill, New
York.
Freeze, R. A., and J. A. Cherry (1979), Groundwater, Prentice-Hall, Engle-
wood Cliffs, N. J.
Freeze, R. A., and P. A. Witherspoon (1967), Theoretical analysis of re-
gional groundwater flow: 2. Effect of water-table configuration and sub-
surface permeability variations, Water Resour. Res., 3, 623–634.
Garven, G. (1985), The role of regional fluid-flow in the genesis of the Pine
Point deposit, Western Canada Sedimentary Basin, Econ. Geol., 80(2),
307–324, doi:10.2113/gsecongeo.80.2.307.
Garven, G., and R. A. Freeze (1984), Theoretical analysis of the role of
groundwater-flow in the genesis of stratabound ore-deposits. 1. Mathemat-
ical and numerical model, Am. J. Sci., 284(10), 10851124, doi:10.2475/
ajs.284.10.1085.
Goode, D. J. (1996), Direct simulation of groundwater age, Water Resour.
Res., 32, 289–296, doi:10.1029/95WR03401.
Figure 13. Vertical distributions of model age through (a) SP 1 and (b) in borehole B2 under different
dispersivities.
W12502 JIANG ET AL. : AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
13 of 14
Hou, G. C., M. S. Zhang, F. Liu, Y. H. Wang, Y. P. Liang, and Z. P. Tao
(2008a), Groundwater Investigation in the Ordos Basin, Geol. Publ.
House, Beijing.
Hou, G. C., Y. P. Liang, X. S. Su, Z. H. Zhao, Z. P. Tao, L. H. Yin, Y. C.
Yang, and X. Y. Wang (2008b), Groundwater systems and resources in
the Ordos Basin, China, Acta Geol. Sin. Engl. Ed., 82(5), 10611069,
doi:10.1111/j.1755-6724.2008.tb00664.x.
Jiang, X. W., L. Wan, X. S. Wang, S. M. Ge, and J. Liu (2009), Effect of
exponential decay in hydraulic conductivity with depth on regional
groundwater flow, Geophys. Res. Lett., 36, L24402, doi :10.1029/2009
GL041251.
Jiang, X. W., X. S. Wang, and L. Wan (2010a), Semi-empirical equations
for the systematic decrease in permeability with depth in porous and frac-
tured media, Hydrogeol. J., 18(4), 839–850, doi:10.1007/s10040-010-
0575-3.
Jiang, X. W., L. Wan, M. B. Cardenas, S. Ge, and X. S. Wang (2010b),
Simultaneous rejuvenation and aging of groundwater in basins due to
depth-decaying hydraulic conductivity and porosity, Geophys. Res. Lett.,
37, L05403, doi :10.1029/2010GL042387.
Jiang, X. W., X. S. Wang, L. Wan, and S. Ge (2011), An analytical study
on stagnant points in nested flow systems in basins with depth-decaying
hydraulic conductivity, Water Resour. Res., 47, W01512, doi:10.1029/
2010WR009346.
Li, Q., K. Ito, Z. Wu, C. S. Lowry, and S. P. Loheide II (2009), COMSOL
Multiphysics: A novel approach to ground water modeling, Ground
Water, 47, 480–487, doi:10.1111/j.1745-6584.2009.00584.x.
Ophori, D. U., and J. To´th (1989), Characterization of ground-water flow
by field mapping and numerical simulation, Ross Creek Basin, Alberta,
Canada, Ground Water, 27(2), 193–201, doi:10.1111/j.1745-6584.1989.
tb00440.x.
Phillips, F. M., and M. C. Castro (2003), Groundwater dating and resi-
dence-time measurements, in Treatise on Geochemistry, edited by H. D.
Holland and K. K. Turekian, Elsevier, New York.
Sanford, R. F. (1994), A quantitative model of ground-water flow during
formation of tabular sandstone uranium deposits, Econ. Geol., 89(2),
341–360, doi:10.2113/gsecongeo.89.2.341.
Sykes, J. F., S. D. Normani, M. R. Jensen, and E. A. Sudicky (2009),
Regional-scale groundwater flow in a Canadian Shield setting, Can. Geo-
tech. J., 46(7), 813–827, doi:10.1139/T09-017.
Tosco, T., R. Sethi, and A. Di Molfetta (2008), An automatic, stagnation
point based algorithm for the delineation of Wellhead Protection Areas,
Water Resour. Res., 44, W07419, doi:10.1029/2007WR006508.
To´th, J. (1963), A theoretical analysis of groundwater flow in small drain-
age basins, J. Geophys. Res., 68, 4795–4812, doi:10.1029/JZ068i008
p02354.
To´th, J. (1980), Cross-formational gravity-flow of groundwater: A mecha-
nism of the transport and accumulation of petroleum (The generalized
hydraulic theory of petroleum migration), in Problems of Petroleum
Migration, edited by, W. H. I. Roberts and R. J. Cordell, pp. 121167,
Am. Assoc. of Pet. Geol., Tulsa, Okla.
To´th, J. (1988), Ground water and hydrocarbon migration, in Hydrogeol-
ogy: Geology of North America, edited by W. Back, J. S. Rosenshein and
P. R. Seaber, pp. 485–502, Geol. Soc. Am., Boulder, Colo.
To
´th, J. (1999), Groundwater as a geologic agent: An overview of the causes,
processes, and manifestations, Hydrogeol. J., 7(1), 114, doi:10.1007/
s100400050176.
To´th, J. (2009), Gravitational Systems of Groundwater Flow: Theory, Eval-
uation and Utilization, Cambridge Univ., Cambridge, U. K.
Wang, X. S., X. W. Jiang, L. Wan, S. Ge, and H. Li (2011), A new analyti-
cal solution of topography-driven flow in a drainage basin with depth-
dependent anisotropy of permeability, Water Resour. Res., 47, W09603,
doi:10.1029/2011WR010507.
Winter, T. C. (1976), Numerical simulation analysis of the interaction of
lakes and ground water, USGS Prof. Pap., 1001, 1–45.
Winter, T. C. (1978), Numerical simulation of steady-state, three-dimen-
sional ground-water flow near lakes, Water Resour. Res., 14, 245–254,
doi:10.1029/WR014i002p00245.
Winter, T. C. (1999), Relation of streams, lakes, and wetlands to ground-
water flow systems, Hydrogeol. J., 7(1), 28–45, doi:10.1007/s1004000
50178.
Winter, T. C., and H. O. Pfannkuch (1984), Effect of anisotropy and ground-
water system geometry on seepage through lakebeds: 2. Numerical simu-
lation analysis, J. Hydrol., 75(1–4), 239–253, doi:10.1016/0022-1694
(84)90052-0.
Yin, L. H., G. C. Hou, Z. P. Tao, and Y. Li (2010), Origin and recharge esti-
mates of groundwater in the ordos plateau, People’s Republic of China,
Environ. Earth Sci., 60, 17311738, doi:10.1007/s12665-009-0310-3.
Yin, L. H., G. C. Hou, X. S. Su, D. Wang, J. Q. Dong, Y. H. Hao, and X. Y.
Wang (2011), Isotopes ( dD and d
18
O) in precipitation, groundwater and
surface water in the Ordos Plateau, China: Implications with respect to
groundwater recharge and circulation, Hydrogeol. J., 19(2), 429–443,
doi:10.1007/s10040-010-0671-4.
Zheng, C., and G. D. Bennett (2002), Applied Contaminant Transport
Modeling, 2nd edition, John Wiley, New York.
W12502 JIANG ET AL.: AGE DISTRIBUTION AROUND STAGNATION POINTS W12502
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... However, a detailed groundwater head, chemistry, and age profiles, the key information for groundwater flow system identification, are hard to obtain in field conditions because the wells used for head measurements and groundwater sampling always have longer filters and mixed groundwater from different depths. For example, Jiang et al. (2012) highlighted the role of groundwater age profiles but only two 14 C data were available in each wellbore. ...
... Numerical modeling of groundwater age distributions in a basin has indicated that inflection points on depth-dependent dating curves could exist at interfaces between flow systems, especially at stagnation points (Jiang et al., 2012). For example, groundwater age in a regional flow system (RFS) or intermediate flow system (IFS) could be several orders of magnitude higher than that in an overlying local flow system (LFS) and subsequently cause a discontinuity in groundwater age at the interface between these systems. ...
... Hydrogeological conditions in the Ordos Plateau are characterized by shallow groundwater in a thin unconfined Quaternary sandy aquifer and relatively deep groundwater in a thick semi-confined Cretaceous sandstone aquifer. Scattered clayey lenses are present in this bedrock aquifer, causing anisotropic properties but do not break the relatively homogeneous feature of the aquifer media at the regional scale (Hou et al., 2008;Jiang et al., 2012). In the lake basins of the study area, the Quaternary aquifer is generally less than 10 m thick. ...
Article
Full-text available
Hierarchically nested groundwater flow systems have been widely investigated by numerical modeling and laboratory experiments but seldom recognized from in situ observations and testing. Groundwater age and geochemical profiles were obtained by the authors using a packer system along two wellbores drilled in the Ordos Plateau, China. Groundwater age profiles were constructed from ³H, ⁸⁵Kr, ¹⁴C, and ⁸¹Kr data, with the apparent age generally increasing with depth, while exhibiting several inflection points. These inflection points were compared with geochemical profiles and numerical modeling results to delineate groundwater flow systems. Inflection points with significant increases in the gradients of age and Cl⁻ concentration versus depth may indicate interfaces among flow systems. A concurrent decrease‐increase turning of groundwater age and Cl⁻ concentration is influenced by a stagnation point. The groundwater age profiles are quite different from previous studies, indicating that the method can greatly reduce the uncertainty in model construction.
... On the other hand, a larger watershed can also increase the rainfall contribution to the intermediate flow, which is ultimately discharged to the low-lying streams. Local and intermediate flow systems are characterized by different groundwater residence times (Jiang et al., 2012). The two asynchronous signals in the baseflow can also interfere with each other. ...
Article
Full-text available
The responses of the nested groundwater flow systems (NGFS) to rainfall fluctuations and the impacts of the NGFS on surface runoff are explored using a fully coupled variably saturated groundwatersurface water model in conjunction with spectral analysis. Numerical experiments are designed to investigate the fractal behaviors of hydraulic head and surface runoff in different scenarios. The results show that the inlets, outlets, and flow patterns of the sub-systems of NGFS can change with rainfall. The scaling-exponent, defined as the slope of the power spectra of the fluctuations of hydraulic head or runoff, is used to depict the fractal behaviors. The scaling-exponent of the hydraulic head is highly variable within the unsaturated zone and local flow systems but remains constant within the intermediate and regional systems. Whether the scaling-exponent of surface runoff exhibits a linear relation with the watershed size depends on the proportion of baseflow in the runoff.
... The position of the surface that separates local and regional flow is a function of hydrography (drainage density) and climate (recharge) (Goderniaux et al., 2013). The presence of local and regional multi-scale flow systems and their associated stagnation points leads to fractal scaling of RTDs (Cardenas & Jiang, 2010;Jiang et al., 2012;Kollet & Maxwell, 2008). Aquifer geometry as well as spatial variation of recharge have been found to result in complex RTD shapes (C. ...
... This process is a direct consequence of basin asymmetry since waters enter a territory of another flow system due to the differences in driving forces and/or geographic position. At the convergence of opposing flow systems under a discharge area, quasi-stagnant zones and hydraulic traps may develop and support heat and dissolved matter accumulation (Anderson and Munter 1981;Jiang et al. 2012;Jiang et al. 2011;Tóth 1987). ...
Article
Full-text available
Extensional domain type geothermal plays, as fertile targets for future resource development, consist of an orogen and an adjoining sedimentary basin of asymmetric physiographic and geologic setting. Preliminary geothermal potential, i.e. prospective geothermal regions, basin-scale flow patterns, heat transfer processes, temperature distribution and appearance of thermal springs were analyzed systematically by numerical simulations in groundwater basins with special emphasis on the effects of basin asymmetry. The importance of basin-scale regional groundwater flow studies in preliminary geothermal potential assessment was demonstrated for synthetic and real-life cases. A simulated series of simplified real systems revealed the effects of anisotropy, asymmetry of the topographical driving force for groundwater flow, basin heterogeneity and basal heat flow on heat accumulation, locations of thermal spring discharge and prevailing mechanisms of heat transfer. As a new aspect in basin-scale groundwater and geothermal studies, basin asymmetry was introduced which has a critical role in discharge and accumulation patterns, thus controlling the location of basin parts bearing the highest geothermal potential. During the reconnaissance phase of geothermal exploration, these conceptual, generalized and simplified groundwater flow and heat transport models can support the identification of prospective areas and planning of shallow and deep geothermal energy utilization, also with respect to reinjection possibilities. Finally, the scope of “geothermal hydrogeology” is defined in a scientific manner for the first time.
... In recent years, the hydrogeological communities all over the world have made new contributions to the field practice and mathematical simulation of groundwater flow systems (Doglioni et al. 2010;Vasić et al. 2019;von Asmuth and Knotters 2004;Xu et al. 2013). Chinese hydrogeologists also successively put forward the concept of groundwater flow since the 1980s (Jiang et al. 2012;Liang et al. 2013;Wang et al. 2017). However, compared with the development of numerical simulation, the progress of laboratory experiments is relatively slow, and there are few studies, which is a weak link in the study of groundwater flow system. ...
Article
Full-text available
Through laboratory data and the analysis of field observation data from the Heihe River Basin in China, groundwater movement (referred to as the groundwater flow) is confirmed, and the groundwater water head value at different vertical depths (in the same aquifer) at any point on the plane differs. When groundwater level rises dynamically, the water head at the lower part of the plane is higher than it is at the head of the upper part; when the groundwater level is dynamically reduced, the upper head is higher than the lower head. That is, the groundwater flow usually moves in an oblique direction, as is the case with the bottom plate. This phenomenon was first observed in laboratory water injection and pumping tests and was verified via the study of water levels at different burial depths for the same aquifer obtained from exploration wells using stratification techniques in the middle reaches of the Heihe River. At the same time, the stratification technology guarantees the practice and field verification of groundwater flow system theory.
Article
Full-text available
Tóthian theory refers to the gravity driven groundwater flow system (GFS) theory represented by Tóth, which mainly expounds the driving and distribution law of groundwater. The establishment and development of this theory not only deepened people’s understanding of the driving and distribution law of groundwater, but also greatly promoted the study of groundwater chemical evolution (GCE). Modern GCE research is mostly based on Tóthian theory, characterized by combining with advanced scientific and technological means. Based on the clue of time, this paper is divided into two parts. The first part mainly summarizes the establishment and development of Tóthian theory, including the exploration of groundwater driving force and distribution form by hydrogeologists before Tóthian theory, and the enrichment, development and application of Tóthian theory by geologists after its establishment. The second part mainly combs the main theories and application progress of GCE mechanism research, including the main theories and findings of GCE research before the emergence of Tóthian theory, as well as the research progresses of GCE after the emergence of Tóthian theory. With the flow of groundwater in GFS, groundwater undergoes continuous chemical evolution, which eventually leads to the transformation of hydrochemical types and the gradual increase of total dissolved solids (TDS). The distribution of GFS and GCE complement each other. The distribution of GFS directly determines the model of GCE, and the results of GCE also play a certain role in the distribution of GFS. GCE mainly includes dissolution, precipitation, cation exchange and adsorption, which is affected by the physical and chemical conditions of permeable media, organic matter content and microorganisms. GCE has the characteristics of universality, sustainability and diversity. With the increasing global population and the progresses of science and technology, the impact of human life, industrial and agricultural production on groundwater is deepening. The aggravation of pollution directly changes the chemical compositions of groundwater, resulting in changes of the law of GCE.
Article
Understanding the circulation and evolution of groundwater and its control mechanism in the Jianghan Plain, which exhibits the complex sedimentary evolution and a progressively deteriorating groundwater environment, is highly imperative and challenging to promote the practical application of groundwater flow system (GFS) and protect the groundwater resources in the region. The aim of this work was to elucidate the evolution pattern of the GFS in the Jianghan Plain and its underlying mechanism. To this end, the grain size characteristics of sediments, geochronological characteristics, stable isotopes in clay porewater, paleoclimate indicators, and existing groundwater age were analyzed to reveal the sedimentary environment of aquifer systems at the basin scale in the study area. It was found that the sedimentary environment changed from one of deep downcutting during the Last Glacial Maximum (LGM) to a fluvial facies that was rapidly infilled with coarse-grained sediments during the last deglaciation period (LDP), and then to a stable lacustrine facies with fine-grained sediments during the Holocene warm period (HWP). These changes were closely linked to the fluctuations of the Yangtze River. Consequently, the existing GFS pattern in the basin presents an unconformable distribution of groundwater age, indicating that it results from the temporal superposition of groundwater flow controlled by the historical sedimentary environment. Dramatic sea level fluctuations since the LGM have resulted in significant changes in the water level of the Yangtze River. This process has impacted the driving force of groundwater, resulting in the evolution of the GFS from a pattern of a fully developed regional GFS during the LGM to the present pattern of a multi-hierarchy nested GFS.
Article
Pores in the subsurface form during the Earth forming process, e.g., sedimentation and diagenesis which evolve over the geologic time scale. Pores serve as the needed ‘room’ for the storage of natural resources and for transporting various fluids. Therefore, quantifying the volume of pores, i.e., the pore volume, is central to many geophysical and engineering problems. However, an accurate determination of subsurface pore volume has remained a challenge, primarily related to the spatial heterogeneity found at multiple length scales. Here, we develop a theoretical framework to quantify the effective pore volume of a multiscale heterogeneous porous matrix and preferential fracture flow system by evaluating groundwater age or residence time of an inert tracer. The robustness of the proposed theoretical model is tested against numerical solutions from a typical fracture (network)-matrix flow system with heterogeneous pore space distribution. We find that, although there are some uncertainties for the application of theory by measuring groundwater age or solute breakthrough curves, our proposed theoretical model is overall robust and insensitive to the length scales with relative errors of less than 9% in estimated effective pore volume. In contrast, traditional methods remain either unrepresentative or lack resolution for determining subsurface pore volume in heterogeneous formations.
Article
Lithium (Li) isotopes have shown large potential in tracing weathering in various water bodies, but there is limited study on Li isotopes in subsurface conditions where CO2 has been largely consumed. In this study, we use a thick sandstone aquifer in the Ordos Basin, NW China, as a natural setting to investigate the behaviors of Li isotopes in hydrogeochemical conditions with different concentrations of dissolved CO2. For young groundwater in the recharge area (group R) where CO2 is abundant (mean PCO2 = 10-2.5 atm), clay formation accompanying with weathering leads to the enrichment of ⁷Li in groundwater. The four deep samples in the recharge area have uniform Li/Na ratios (with a mean of 2.52 μmol/mmol) and δ⁷Li (with a mean of 25.0‰), corresponding to a mean Li removal rate of 81.2% compared with the sandstone leachate. For groundwater in the shallow part of the discharge area (group D1), Li was firstly removed by clay formation during weathering in the recharge area and was later removed by physisorption when CO2 becomes much lower (mean PCO2 = 10-3.1 atm). Different degrees of weathering lead to a wide range of δ⁷Li varying from 19.7‰ in the deepest well to 33.0‰ in the shallowest well. The proportion of Li removal caused by physisorption is found to increase with groundwater age. After the stage of Li removal by adsorption, Li was released in the deeper part of the discharge area (group D2), and the positive correlation of δ⁷Li versus Li/Na is explained by a ternary mixing model. The endmember of water brought by cation exchange is inferred to have a heavier δ⁷Li than sandstone leachate, demonstrating that cation exchange could cause an enrichment of ⁷Li in water. This study enhances our understanding of the controlling factors of Li isotopes in deep groundwater with low dissolved CO2, which have implications for the application of Li isotopes in subsurface water.
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Numerical models with spatially-varying head as top boundary conditions were used in previous studies to understand topography-driven groundwater flow. The head boundary conditions could cause artifacts of extremely large, but unrealistic recharge rates owing to unlimited supply of water. This study adopted a fully-coupled surface–subsurface hydrologic modeling approach to simulate transient topography-driven groundwater flow and also surface-water flow under homogeneous and isotropic settings. Two 100-year climate datasets and five hydraulic conductivities (K, 0.01 - 100 m/d) were tested in numerical experiments. In the base case with a wet climate (annual precipitation 1696 mm/y) and K of 1 m/d, groundwater head at two different locations close to both lateral boundaries fluctuates only within 5.1 m and 9.6 m, respectively, during the 100-year period. Despite the local water table fluctuations caused by the variability in the climatic record, large-scale groundwater flow systems can be assumed in dynamic equilibrium provided stationary climate. Long-term average exchange fluxes are spatially constant and limited by precipitation infiltration when surface water is absent, whereas they vary from positive to negative values (i.e., recharge to discharge) spatially when surface water is present. Sensitivity analysis suggests that wetter climate and smaller K lead to more inundation of the land surface, stronger hierarchical nesting of groundwater flow systems and more variable exchange fluxes. Overall, our first fully-coupled modeling of topography-driven groundwater flow implies that attention must be paid to causality between head and flow, and climatic record as boundary conditions may be more appropriate due to its relaxed manner.
Book
This book deals with the problems and methods of paleohydrogeolo gy in relation to ore deposit studies. It presents a description of dif ferent techniques used in the course of structural-paleohydrogeologi cal, paleo hydrogeochemical and paleo hydro geothermal investiga tions. It also provides itlformation on the regular, regional patterns of formation and subsequent distribution of ground water within dif ferent shells of the Earth. The main aspects of metal content of ground water and contemporary processes of ore genesis are discuss ed. Ore deposits are classified according to paleohydrogeological con ditions under which they were formed. The readers are acquainted with paleohydrogeological analysis of these conditions for different types of ore deposits, namely (1) ore deposits formed in artesian basins, in which sedimentary rocks were predominant both at the time of magmatic activity and in the periods free of this activity; (2) ore deposits formed in artesian, ad artesian basins (and admassifs) characterized by extensive development of volcanic rocks and magmatic activity; (3) ore deposits that originated in hydrogeological massifs (and admassifs) in the process of formation of linear weather ing crusts. This book, which should be of great interest to geologists engaged in prospecting for and exploration and study of ore minerals, also in cludes 38 tables, 60 illustrations and a bibliography of 450 titles. EVGENY A. BASKOV Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 The Science of Paleohydrogeology and Its Objectives in Ore Deposit Studies . . . . . . . . . . . . . . . . 4 2 Principal Distribution Patterns of Contemporary Ground Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2. 1 Notion of Hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . ."
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This book recognises groundwater flow as a fundamental geologic agent, and presents a wide-ranging and illustrated overview of its history, principles, scientific consequences and practical utilization. The author, one of the founding fathers of modern hydrogeology, highlights key interrelationships between seemingly disparate processes and systems by tracing them to a common root cause - gravity-driven groundwater flow. Numerous examples demonstrate practical applications in a diverse range of subjects, including land-use planning, environment protection, wetland ecology, agriculture, forestry, geotechnical engineering, nuclear-waste disposal, mineral and petroleum exploration, and geothermal heat flow. The book contains numerous user-friendly features for a multidisciplinary readership, including full explanations of the relevant mathematics, emphasis on the physical meaning of the equations, and an extensive glossary. It is a key reference for researchers, consultants and advanced students of hydrogeology and reservoir engineering. © J. Tóth 2009 and Cambridge University Press, 2009. All rights reserved.
Article
This work highlights the lack of unique solutions for regional groundwater flow models and quantifies the degree of freedom concerning hydraulic conductivities for models calibrated on measured hydraulic heads. The potential of 4He as an independent tracer at reducing the nonuniqueness problem is tested. Four different calibrated groundwater flow scenarios are presented for the Carrizo aquifer and surrounding formations in Texas. It is shown that variations of hydraulic conductivities up to 2 orders of magnitude in the Carrizo aquifer and overlying confining layer lead to similar calculated hydraulic heads. No clear-cut arguments are present to invalidate one groundwater flow scenario over a different one. In contrast, when tested with a 4He transport conceptual model, all groundwater flow scenarios except one failed to reproduce a coherent 4He transport behavior in the system. This study exemplifies possible future contributions of 4He at discerning which model most closely replicates natural conditions.
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The role of gravity-driven ground-water flow in the genesis of epigenetic stratabound ores in sedimentary basins is subjected to quantitative analysis. Numerical modelling techniques are applied to solution of theoretical equations governing fluid flow, heat and mass transport, and geochemical reaction paths. The physics of transport processes and possible hydrodynamic constraints are particularly emphasized. A computer code for simulation of regional transport processes along 2-D cross-sections across sedimentary basins is developed. A simulation example is presented which demonstrates that gravity-flow systems are capable of providing favourable conditions for ore formation near the edge of a basin.-M.S.
Article
The sensitivity to change in the numerical value of a given parameter in quantitative modelling of transport processes is assessed for a variety of hypothetical cross-sections. It is demonstrated that ground-water-flow systems could be responsible for conditions favourable to ore formation at ground-water discharge areas near the edge of a sedimentary basin. (Preceding abstract)-M.S.
Article
Theoretically, three types of flow systems may occur in a small basin: local, intermediate, and regional. The local systems are separated by subvertical boundaries, and the systems of different order are separated by subhorizontal boundaries. The higher the topographic relief, the greater is the importance of the local systems. The flow lines of large unconfined flow systems do not cross major topographic features. Stagnant bodies of groundwater occur at points where flow systems meet or branch. Recharge and discharge areas alternate; thus only part of the basin will contribute to the baseflow of its main stream. Motion of groundwater is sluggish or nil under extended flat areas, with little chance of the water being freshened. Water level fluctuations decrease with depth, and only a small percentage of the total volume of the groundwater in the basin participates in the hydrologic cycle.