International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
The Application of Numerical Simulation on Groundwater
Yield Calculation of Seepage Well
Xu Jialu1, Wang Wei2
1,2
School of Environmental Science and Engineering, Chang’an University, No. 126 Yanta Road,
Xi’an 710054, China
1,2
Key Laboratory of Subsurface Hydrology and Ecology in Arid Areas, Ministry of Education, No.126 Yanta Road,
Xi’an 710054, China
Seepage wells have the following advantages over
traditional vertical wells: the drawdown is lower,
groundwater tends to enter the wells at low velocities, the
wells do not need frequent cleaning, and the operating cost
of the wells tends to be low(Bakker et al., 2005). Owing to
these benefits, in recent years, seepage wells have attracted
considerable attention as groundwater supply wells. A
number of studies on seepage wells have been carried out.
Therefore, in this paper a methodology of numerical model
is developed to construct the seepage well. The proposed
model is applied in Zaolinping Village which locates at
Shenmu County, China.
Abstract—In regions where rivers are not perennial or have
low flow conditions during most part of the year(like banks of
the Yellow River), the seepage wells are placed in the riverbed
to obtain uninterrupted supply of naturally filtered
groundwater through highly permeable saturated riverbed
aquifers. Due to the complexities of flow, no exact analytical
solution exists to provide steady state discharge drawdown
relationship for seepage well. To overcome this difficulty, in
this study a numerical model was developed for seepage well
by adapting the equivalent hydraulic conductivity and the
coupled seepage-pipe flow model. The numerical model is
proposed to be applied for groundwater exploitation in
Zaolinping Village which locates at Shenmu County, China.
By calculation, the water yield of study area is 47600 m3/d.
The results show that the proposed methodology based on the
application of the coupled seepage-pipe flow model has been
found to be efficient in constructing riverbed aquifer model
with seepage well, which has a positive theoretical significance
for guiding the design and construction of seepage well.
II. FLOW CHARACTERISTICS OF SEEPAGE WELL
Diverse flow regimes coexist in the seepage well system.
Usually the groundwater flow through a porous medium is
laminar flow with low Reynolds number(Re<1~10), which
can be explained on the basis of mass conservation and
Darcy’s law. In contrast, flow within a well pipe with great
hydraulic radius and great Reynolds number can not be
represented on the basis of Darcy’s law, which is only valid
for laminar flows, thus other flow regimes can not be
expressed.
The quantity of water intake is mostly from saturated
riverbed aquifer in the early days, while the river
infiltration is little. With the continuation of work time, the
water level of the aquifer is lower than that of the river,
then the river infiltration increases. When the pumping
intensity is not too large and the seepage well system reach
a steady state in a short period of time, the quantity of
water intake is almost entirely from the river leakage
supply. Groundwater flow around a seepage well has
significant three dimensional flow characteristics.
Keywords—seepage well, equivalent hydraulic conductivity,
the coupled seepage-pipe flow model, groundwater yield
I. INTRODUCTION
The Quaternary alluvium of the Yellow River Valley is
relatively thick with good permeability. Under the leakage
recharge by the Yellow River, it is a favorable water source
for centralized water supply. However, the water yield
produced by traditional vertical wells is small, which can
not meet the need of urban water consumption. According
to the experience of regions with similar conditions,
seepage wells can be adopted as the method for
groundwater exploitation at the banks of the Yellow River.
A seepage well consists of a vertical well, chamber,
gallery and a number of radiation holes. Each seepage well
has several chambers to which the radiation holes are
connected. The radiation holes spread laterally through an
aquifer and collect water when groundwater abstraction
occurs at the vertical well. Usually the vertical well is
constructed at the bank of the river with a depth of 20-30m,
which is the water intake of seepage well.
III. CALCULATION MODEL OF SEEPAGE WELL
Due to the complex flow characteristics, it is difficult to
describe the boundary condition of the seepage well
system.
6
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
Chen et al. proposed a new numerical approach that a
well can be represented by an equivalent hydraulic
conductivity that depends on the Reynolds number within
the pipe, which is called the coupled seepage-pipe flow
model. According to the coupled seepage-pipe flow model,
different flow regimes can be expressed and connected by
the equivalent hydraulic conductivity.
When the water flow is laminar flow, the equivalent
hydraulic conductivity Kl in the “well pipe” can be
expressed as:
Kl=
d 2
32 
When the water flow is turbulent flow, the equivalent
hydraulic conductivity Kn in the well pipe can be expressed
as:
Kn=
2 gd
fv
(2)
Where g is the acceleration due to gravity, f is the
coefficient of friction,  is the seepage velocity in well
pipe.
From the formula above, the flow law of a seepage well
system can be expressed as the form of Darcy’s law, which
means that the seepage flow can be coupled with the pipe
flow. Thus a numerical model for seepage well is
constructed:
(1)
Where  is heavy rate of water, d is equivalent diameter
of the well pipe  is the dynamic viscosity coefficient of
water.
 
H   
H   
H 
   K ve
   K he
  0  x, y , z   D
  K he
x  y 
y  z 
z 
 x 


 H |  0
zero flow boundary
 n 2

 K r H r  H   qr
river boundary
Mr

exchange flow between pipe and aquifer
Qe  C H p  H 

d 2 d 2 g H


laminar flow



 4 32 l


0.25
1.75

d 2 2 gd  d   1  H

smooth turbulent flow  pipe flow
   
Q p  
l
 4 0.316     v 


2
d 2


d  1 H




8 gd   log10 3.71  
rough turbulent flow
 4

e v l



H  z 

 H
water table boundary


0



n

 p
 H  x, y , z   H
vertical well boundary
s

K
K e= 
Kl
Kn

hydraulic conductivity in aquifer medium, laminar flow
equivalent hydraulic conductivity in" WellPipe" , laminar flow
equivalent hydraulic conductivity in" WellPipe" , turbulent flow
7
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
Where H is head; K is hydraulic conductivity; n is
exterior normal vector of the second boundry; np is internal
normal vector of the water table boundary; C is the
conductance of pipe screen material; Qe is the exchange
flow rate between well pipe and aquifer; Qp is the flow rate
in well pipe; Kr is the vertical hydraulic conductivity of
medium in riverbed; Mr is the thickness of medium in
riverbed; qr is specific river leakage; q is the specific flow
Under the condition of riverside exploitation, the
stimulated leakage of the Yellow River becomes the
dominating recharge source, and the manual exploitation is
the major discharge(Chen Chongxi et al.,2008). According
to the experience of regions with similar conditions,
seepage wells can be adopted as the method for
groundwater exploitation at the banks of the Yellow River.
To depict the complex structure of the seepage well
accurately, rectangular units are used in the fine
discretization of the calculation domain. Zaolinping model
area is discretized into 300 columns along the east-to-west
direction and 602 rows along the north-to-south direction.
The horizontal interval of the discretization grid is 5m. The
number of active cells in a single-layer is 75502, and the
horizontal area actually represented is 1888000m2. The
model domain is subdivided into 11 layers vertically; in
which the Quaternary aquifer is discretized into 3 layers
and the bedrock fractured aquifer is discretized into 8
layers. Thus, the total number of active cells is 830522.
According to local hydrogeology conditions, seven
seepage wells(two vertical wells are 400m apart) are laid in
the study area. Each seepage well has five chambers and
the spacing between two chambers is 60m or 70m. A threedimensional finite difference method is used to calculate
the water yield of the study area when the drawdown of
seepage well is 5m. The calculation results are shown in
Table I. The total yield in the normal is 61300 m3/d and the
steady state flow fields under the pumping of 7 seepage
wells is shown in Fig I.
rate of the second boundry of per unit area;  H is head
loss and υ is fluid viscosity coefficient.
IV. APPLICATION
The study area is located in Shenmu County, Shaanxi
Province, China, longitude110°50′, latitude38°83′, where
the aquifer medium is mainly Quaternary Holocene gravel
layer and Triassic clastic bedrock weathering zone. The
Yellow River lies on the northeast of the study area. Under
natural conditions, the groundwater discharges to the
Yellow River after the areal precipitation infiltration
recharge; under the conditions of future exploitation,
massive exploitation of groundwater will stimulate massive
leakage recharge of the Yellow River. Thus the Yellow
River can be conceptualized as the third kind of boundary.
The southwest boundary of the study area is the interface
between Mesozoic bedrock and alluvia of the river valley,
which can be conceptualized as the non-flow boundary due
to underdeveloped fractures of Mesozoic bedrock; the
bottom surface is complete Mesozoic bedrock constituting
regional impervious base. Under natural conditions, after
being recharged through the infiltration of precipitation,
groundwater is flowing from west to the east on the whole
and finally discharging into the Yellow River.
8
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
Table I.
Results of simulation for Seepage Well’s Pumpage
Water yield composition(m3/d)
Well
number
Total
yield(m3/d)
Proposed
yield(m3/d)
Chamber1
Chamber2
Chamber3
Chamber4
Chamber5
gallery
Vertical well
ZLP1
2399.8
1867.3
1874.4
1831.8
2338.8
25.2
14.6
10352
10300
ZLP2
2247.7
1565.9
1602.8
1765.5
2304.1
25.8
13.5
9527.1
9500
ZLP3
2676
2105.6
2109.8
2101.6
3419.7
37.4
16.4
12466.6
12400
ZLP4
2677.7
2111.6
2084.5
2086.3
2670.4
37
16.4
11683.9
11600
ZLP5
687.3
559.2
1646.3
2022
2509.2
32.2
9.3
7465.6
7400
ZLP6
1434.1
734.5
558.9
549.1
634.2
34.9
9.7
3955.4
3900
ZLP7
1377.5
1115.8
1134
1145.5
1402.9
42.5
12.9
6232.2
6200
61682.7
61300
Total wells
As the recession of water boundary of the Yellow River
in the dry season, the water yield will decrease obviously.
In order to calculate the water yield of seepage wells during
the dry season, reset the condition of water boundary and
water level in the model. Thus the water yield in the dry
season can be calculated. The results show that the total
yield in the dry season is 47600m3/d, decreases by 22.07%.
With a storage facility, the infiltration replenishment of the
river in the normal season can be stored, which can be used
in the dry season, thus the water utilization rate of the
region will increase markedly.
V. CONCLUSIONS
A coupled seepage-pipe flow model for seepage well
was proposed by introducing the concept of equivalent
hydraulic conductivity. The proposed model was applied in
Zaolinping Village for water supply field of seepage wells.
The water yield of study area was calculated by adopting
the three-dimensional groundwater flow finite difference
method. The total water yield is 61300m3/d in the normal
season, which is 47600m3/d in the dry season. The results
show that the mathematic model can greatly reflect the
flow characteristics of seepage well.
Fig I. Drawdown contour map of seepage wells, normal season
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)
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