Download 2D-Modeling of flow processes in the unsaturated

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II Natural and Human influences on groundwater
2D-Modeling of flow processes in the unsaturated zone of wetlands
Barbara EULER & Oliver KEMMESIES & 1) Peter-Wolfgang GRAEBER 2)
1) KP Ingenieurgesellschaft für Wasser und Boden mbH, Bahnhofstraße 37, D-91710 Gunzenhausen, Germany
2) Institute of Waste Management and Contaminated Sites, Technische Universität Dresden, Pratzschwitzer
Straße 15. D-01796 Pirna, Germany
ABSTRACT
The exploitation of water resources, which is the base of a secure drinking water supply, is based on certain
calculation rules and estimates from the past. Nevertheless climatic changes are nowadays already observed and
for the future expected. One expected change is the increase of extreme precipitation events with high intensity.
It is foreseeable, that under these conditions even, if the mean precipitation amount should remain constant, the
groundwater recharge will decrease, because of the limited infiltration capacity of soil. A further problem is the
increasing cultivation of energy crops which cause a higher evapotranspiration and remove additionally water
from the soil. Taking all these different aspects into account, it can be said that the result is an enhancement of
surface run-off and in the end a minimization of groundwater recharge. The creation of synthetic wetlands might
be a solution to this problem. Wetlands are areas which feature less surface run-off and a high infiltration capacity. Therefore it is possible to increase the groundwater recharge in an area with lack of groundwater by creation
and optimization of wetland-zones. The main features of the soil in wetlands areas are a high hydraulic conductivity as well as a high storage coefficient. Soil erosion is avoided by a vegetation cover, which features a low
evpotranspiration. It is strong recommended to use a 2D-vertical-plane flow model to optimize the construction
of such wetlands. For this purpose we developed the simulation program SiWaPro DSS. It is able to describe the
required complex properties of soil and the interaction between vegetation and soil. The simulation program
SiWaPro DSS is also coupled with a stochastic weather generator.
Keywords: Richards equation, van-Genuchten parameter, wetlands, water managment
Decrease of Groundwater Recharge
The exploitation of water resources is the base of a secure drinking water supply. Today up to 80 % of
groundwater is used as drinking water in arid areas (BFAI, 2006). According to the directive 98/83/EC
of the European Union, water shall not contain any concentration of micro-organisms, parasites or any
other substance which constitutes a potential human health risk. The free admission for everyone to
drinking water and a secure supply of water should be ensured anytime.
Today many countries with arid climate conditions have problems to meet these demands. Accelerated
population growth and non-sustainable (ground) water management can have an additional negative
effect. Due to the imbalance between pumping and recharge the groundwater levels decline step by
step consequently. The climatic change can cause these phenomena in areas too, where today the people are still not faced with the problem of lack of water. That is why solutions have to be developed to
secure the supply of groundwater used for drinking today and in the future.
A sustainable water management is very important in arid and semiarid areas where geographic position and climatic conditions cause a permanent lack of water. The climatic conditions of these areas
are featured by precipitation events which occur in intervals. But these precipitation events are not
able to refill the groundwater storage because of the limited infiltration capacity of soils. This aspect
can be increased by a lack of vegetation caused by deforestation and overgrazing. Taking all these
different aspects into account, it can be said that, the result is an enhancement of surface run-off, and a
reduction of groundwater recharge.
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The water problem is increased by enhanced population growth and urbanization. Moreover the increasing cultivation of ‘thirsty’ plants, like cotton wool burdens the water supply. Additionally, the
evaporation removes water from the soil. Over-irrigation and inefficient use are further aspects that
endanger the water balance.
Groundwater Recharge in Artificial Wetlands
An innovative approach is the artificial recharge of groundwater. The artificial groundwater recharge
can be done using infiltration ponds or even wetlands. In general natural wetlands are divided in
coastal and inland wetlands. The inland wetlands are located along rivers, streams, margins of lakes
and ponds or in depressions. Most of them are seasonal (EPA, 2004). Wetlands are a transition zone
between the surface and the groundwater. They are areas which feature less surface run-off and a high
infiltration capacity. Moreover the plants in wetland can soak up the chemicals from the groundwater
that might contaminate it (Science Update, 2007). A high ratio of infiltration capacity and hydraulic
conductivity as well as a high storage coefficient can increase the groundwater recharge. Evaporation
and vegetation reduce it.
Fig.1Parameters of Groundwater Recharge
The construction of a artificial wetland and the following optimization of these wetlands leads to a
maximum of groundwater recharge under the given environmental conditions. The useable water resources for an infiltration in wetlands are precipitation, cleaned wastewater and water of rivers, lakes
and dams. The groundwater recharge depends on the features of climate, soil and vegetation in these
areas. The properties of soil and vegetation have to be optimized to ensure a maximum infiltration.
The advantages of optimized artificial groundwater recharge areas, that are modelled on wetlands, are:
F minimum construction effort
F no complex technology
F low costs
F low maintenance
F cleaning of water by natural attenuation
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F reduced evapotranspiration deficit
F water protected against contamination
Flow Processes in the Unsaturated Zone
The processes in the unsaturated zone are intended to identify and figured by different models.
There are different approaches to describe the flow processes in the unsaturated zone. A deterministic
approach is the Richards equation (1a+b). This equation represents the connection between the water
flow, caused by a potential gradient, and the change in water content of a soil volume per time unit.
and
⎛ ∂h p
⎞ ⎞ ∂θ
∂ ⎛⎜
k (θ) ⋅ ⎜⎜
− w0
+ 1⎟⎟ ⎟ =
⎜
⎟
∂r ⎝
⎝ ∂r
⎠ ⎠ ∂t
(1a)
∂h p
∂θ
= C(h c ) ⋅
∂t
∂t
(1b)
The independent variables are time t and spatial coordinate (x,y,z). The dependent variables of equation (1) are the water pressure head hp and the water content θ. w0 is defined as the sink/source term.
The capillary capacity function C(hc) is the first derivative of the hysteretic soil water retention curve.
The unsaturated hydraulic conductivity k(θ) depends on the water content in the soil.
Soil Retention Curve
The capillary capacity function C(hc) and the unsaturated hydraulic conductivity k(θ) are implemented in the Richards equation. Both are van-Genuchten-Parameter-functions called after the model
on which they base. In the following a modified version, the hysteretic parametric model by van Genuchten (1980) and Luckner et al. (1989) is given:
θW = A +
φ − A −B
[1 + (α ⋅ h ) ]
1
n 1− n
hc > 0
(2a)
hc ≤ 0.
(2b)
c
θW = φ − B
The parameters of equation 2a and 2b are porosity φ, residual wetting fluid content θW,r, residual air
content θA,r, scaling factor α, and slope parameter n. Figure 2 shows a typical curve set for this hysteretic function.
To describe these different curves, the variable A as a function of the residual wetting fluid content
A=A(θW,r), the variable B as a function of the residual air content B = B(θA,r), and the scaling factors α
and α i for the drainage and imbibition branches, respectively, were introduced. A detailed description of the parametric model, which differs from the original work of van Genuchten (1980), is given
by Luckner et al. (1989), Nimmo (1991), Luckner et al. (1991), Nielsen and Luckner (1992) and Kemmesies (1995).
d
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capillary pressure head in cm
0
5
10
15
20
25
30
35
40
45
50
0.40
porosity φ = 0.36
Be=0.144
wetting fluid content
0.35
0.30
residual non wetting fluid content Bd=Bf-g=θNW,r=0.10
0.25
0.20
f
0.15
Ad=0.113
0.10
0.05
e
d
c
d
c e
f
g g
PDC - Primary Drainage Curve
SWC - Scanning Wetting Curve
SDC - Scanning Drainage Curve
MWC - Main Wetting Curve
MDC - Main Drainage Curve
residual wetting fluid content Ac = Ae-g = θW,r= 0.05
0.00
0
500
1000 1500 2000 2500 3000 3500 4000 4500 5000
capillary pressure in Pa
Fig. 2 Example of a Hysteretic Soil Water Retention Curve
Relative Permeability Function
The parameter function of the unsaturated hydraulic conductivity k(θ) was modeled by Mualem (1976)
and Luckner et al. (1989) with
⎛ S ⎞
k (θ) = k 0 ⋅ ⎜⎜ ⎟⎟
⎝ S0 ⎠
λ
m
1
⎤
⎡ ⎛
m ⎞
⎢1 − ⎜ 1 − S ⎟ ⎥
⎠ ⎥
⋅⎢ ⎝
m
1
⎥
⎢ ⎛
m ⎞
⎢1 − ⎜ 1 − S 0 ⎟ ⎥
⎠ ⎦
⎣ ⎝
2
3)
Parameters of eq. 3 are the hydraulic conductivity k0(θ0) at a matching point (0) with a known degree
of wetting fluid mobility S 0 =(θ0-θW,r)/(φ- θW,r), the connectivity parameter λ and the transformation
parameter m. An example of the function is shown in figure 3.
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mobility degree
0.00
0.25
0.50
0.75
1.00
relative permeability
1.0
0.8
–
S0 = 1.0
–
S0 = 0.86
0.6
0.4
0.2
0.0
0.00
0.06
0.12
0.18
0.24
0.30
0.36
wetting fluid content
Fig. 3 Example of a Relative Permeability Function
Water mangament
Traditionally water resources management till now has been practically performed for surface water
flows. It has been realized mainly by reservoir operation for both ordinary water use and flood prevention. The management task is expressed in an optimized hierarchical distribution of water volumes
between different water users for an annual or seasonal time interval.
During the last two decades the problem of integrated water management has reached a certain level of
development. Groundwater management for instance is very important because of observed trends of
water supply deficiencies and of possibilities to use water for irrigation purposes more economically.
Regulating groundwater table contributes to the solution of diverse ecological problems. The general
concept of groundwater management is based on controlled drainage according to available water
resources in the region. The classical drainage facilities are ditches, open channels, drainage pipes,
mole drainage and vertical drainage wells, providing mainly subsurface drainage. Water management
systems are set up in various configurations. The drainage facilities should be operated alternately for
the management purposes.
Investigations on water management systems useable for subsurface irrigation have been carried out in
different countries: Slovakia, Russia, the Netherlands, Poland, Bulgaria, Germany, the USA, the
Ukraine and elsewhere. In most cases the attention has been focused on drainage equipment operation
and on possibilities of maintaining a certain groundwater level, or on determining the drainage water
amount under constant operation conditions. The results of investigations and practical applications
clearly confirm the possibility of regulating the groundwater level by means of drainage equipment.
These results are only the basis for new research work on a complex of problems depending on requirements for control systems operating under dynamically changing conditions and still meeting the
needs of water users.
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Modeling of flow processes using SiWaPro DSS
A computer based Decision Support System including computer simulation tools with active graphical
user interface is the basis for the modern water management. Since the unsaturated zone is considered
the use of 2D-vertical-plane models are recommended. To obtain a maximum groundwater recharge or
rather to optimize an artificial wetland, the processes in the unsaturated zone have to be calculated and
described by these models. The simulation program SiWaPro DSS is able to compute the two dimensional vertical plane and rotationally symmetric flow and transportation processes including the degradation and sorption in the un/saturated zone.
2. Modeling of Flow and Transport Processes
Transfer of Measurement
2 3
1
3. Optimization of Groundwater Recharge
4
1. Measurement
of Soil Parameters
On/Off
Enter
2 3
1
4
O n/O ff
Enter
Artificial Groundwater Recharge Area
Leachate
Groundwater
Unsaturated Zone
Saturated Zone
.
Fig. 4 Modeling and Optimization
The title of the program is the german synonym for Sickerwasserprognose (leachate prognosis) Decision Support System. The software was developed by the Technical University Dresden in cooperation with the KP Society of Engineers for Water and Soil mbH. It serves as a tool for risk assessment.
The Richards Equation and the van-Genuchten-parameter functions are implemented in the simulation
program SiWaPro DSS. The program based on the commonly used simulation code SWMS_2D
(Šimunek et al., 1994) and solves the Richards-equation using the Finite-Elements method (Kemmesies, 1995).
Furthermore the software has the ability to simulate solute transport in the unsaturated zone based on
the convection-dispersion equation. Therefore the risk of a possible contamination of groundwater can
be estimated and a contamination avoided. For this reason a contaminant database is implemented.
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An implemented weather generator simulates the time series of precipitation, solar radiation and the
parameter evapotranspiration (Nitsch et al., 2007). A soil database is implemented in SiWaPro DSS,
too.
In figure 5 a simulation of the flow and transport processes with SiWaPro DSS is shown.
The simulation program SiWaPro DSS is able to calculate and describe the existing complex properties of soil and the interaction between vegetation and soil in wetlands. Therefore the program can
calculate and optimize the water processes in a groundwater recharge area.
Fig.5 Simulation run
Literature
BFAI (2006):
Regionale Engpässe in der Wasserversorgung Syriens. Bundesagentur für Außenwirtschaft. –
Servicestelle des Bundesministeriums für Wirtschaft und Technologie (Germany),
http://www.bfai.de/
EPA (2004):Wetlands Overview. Office of Water.
http://www.epa.gov/owow/wetlands/pdf/overview.pdf
Kemmesies, O. (1995): Prozeßmodellierung und Parameteridentifikation von Mehrphasenströmungsprozessen in porösen Medien. Dissertation. Fakultät für Geowissenschaften, Geotechnik und Bergbau der TU Bergakademie Freiberg. Proceedings des Dresdner Grundwasserforschungszentrum e.V.. Heft 7. Dresden. ISSN 1430-0176.
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Luckner L., van Genuchten, M.Th., Nielsen, D.R. (1989): A Consistent Set of Parametric Models for
the Two-Phase Flow of Immiscible Fluids in the Subsurface. Water Resour. Res. 25(10): p.
2187-2193.
Luckner L., van Genuchten, M.Th., Nielsen, D.R. (1991): Reply to NIMMO's "Comment on the
Treatment ....". Water Resour. Res. 27(4): p. 661-662.
Mualem, Y. (1976): A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous
Media. Water Resour. Res. 12: p. 513-522.
Nimmo, J.R. (1991): Comment on the Treatment of Residual Water Content in "A Consistent Set of
Parametric Models for the Two-Phase Flow of Immiscible Fluids in the Subsurface" by L.
Luckner et al.. Water Resour. Res. 27(4): p. 661-662.
Nitsch, B., Gräber, P.-W., Kemmesies, O. (2007): Anwendung synthetischer Niederschlagszeitreihen
bei der Strömungssimulation in der ungesättigten Bodenzone. TU Dresden, Dresden, Workshop
2007-Simulationen in Umwelt-und Geowissenschaften, Shaker Verlag
Nielsen, D. R., Luckner, L (1992): Theoretical aspects to estimate reasonable initial parameters and
range limits in indentification procedures for soil hydraulic properties. In, Proc. Intl. Workshop
on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, edited by M.
Th van Genuchten, F. J. Leij, and L. J. Lund, University of California, Riverside, pp. 147-160.
Science Update (2007): http://www.sciencenetlinks.com/sci_update.cfm?DocID=262
Šimunek, Vogel, J.T., van Genuchten, M. Th.; (1994): The SWMS_2D code for simulating water flow
and solute transport in two-dimensional variably saturated media, Version 1.1., Research Report
No.132, U. S. Salinity Laboratory, USDA, ARS, Riverside, CA.
van Genuchten, M.Th. (1980): A Closed-form Equation for Predicting the Hydraulic Conductivity of
Unsaturated Soils. Soil Sci. Soc. Am. J. 44: p. 892-898.