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Scientific Bulletin of the Politehnica University of Timisoara

Transactions on Mechanics Special issue

The 6th International Conference on Hydraulic Machinery and Hydrodynamics Timisoara, Romania, October 21 - 22, 2004

GROUDWATER HYDRAULICS APPLIED TO THE LETEA FOREST ECOSYSTEM

FROM THE DANUBE DELTA

Virgil PETRESCU*, Professor, Ph.D., Hydraulics and Environmental Protection

Department, Technical University of Civil Engineering Bucharest

Alexandru DIMACHE, Lecturer, Ph.D., Hydraulics and Environmental Protection

Department, Technical University of Civil Engineering Bucharest

Nicolai SÎRBU, Lecturer, Ph.D. Hydraulics Structures Department,

Technical University of Civil Engineering Bucharest

*Corresponding author: Bd. Lacul Tei No.124, Sector 2, Bucureşti, Romania Tel./fax: (+40) 21 2433660, Mobile: (+40) 745 303 686, Email: vap@hidraulica.utcb.ro

ABSTRACT The Letea forest ecosystem, situated in the Danube Delta Biosphere Reservation, between the Chilia and Sulina branches, has imposed, within the framework of the ecological recovery, the carrying out of certain research activities concerning the current state of the environment, and, respectively, the interdependency of the surface and groundwater regime, climatic, pollution control, relief and soil conditions, in accor-dance with the 2000 /60 / CE Frame Directive (“The action framework in the water policy domain”).

KEYWORDS

Forest ecosystem, groundwater, mathematical model, pollutant dispersion, evapotranspiration process.

NOMENCLATURE Ss [1/m] specific storage coefficient H [m] pressure head K [m/s] tensor of the hydraulic conductivity coefficients kxx, kyy, kzz [m/s] components of the hydraulic conductivity coefficients along the coordinate axes x, y, z, respectively Ki [m2] intrinsic permeability coefficient t [s] time W [1/s] flow sources related to the unit volume (water withdrawal and/or injection) ρ [kg/m3] water density g [m/s2] gravitational acceleration µ [kg/(ms)] dynamic viscosity coefficient for water

q [m/s] specific discharge vector (on the unit surface) v [m/s] velocity vector C [kg/m3] mass concentration Cs [kg/m3] mass concentration at the source ne [-] effective porosity D [m2/s] dispersion tensor (of the hydrodynamic dispersion coefficients).

1. INTRODUCTION The Letea forest from the Danube Delta (figure 1) has an overall surface of 5,396 ha, out of which the integral protected area is of about 2,800 ha (figure 2). It has been under protection since 1930 (together with the Caraorman forest), and since 1938 it has been declared a natural reservation. The Letea forest has been included in the international UNESCO biosphere reservations network at the 4th Session of the International Council for the Coordination of the Man and Biosphere Program (MAB), Paris, November 1979. Only research and documentation activities are allowed inside the integral protected area, while keeping in focus the uniqueness of the forest ecosystem, with century old oak, poplar and ash trees raised on fluvial-maritime sandy islands having phreatic water at the soil surface or near by, and with more than 100 mammal, bird, reptile, amphib-ian and invertebrate protected species [1, 2]. As a result of the execution of several hydro technical works in the vicinity of the protected area, works done considering other purposes (flood protection for the Periprava, Letea and C. A. Rosetti settlements, fish

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Figure 1. The Danube Delta, oversight. Figure 2. The Letea protected area.

farm Popina, etc.), the Letea forest has been separated from the influence of the natural Danube’s flooding regime. Thus, the cut-off from the natural soil regen-eration by the Danube’s alluvia and the salt concen-tration increase in the soil, due to the evapotranspiration (800 mm / year) being greater than precipitation (320 mm / year), occur. These are phenomena, which may constitute limiting factors of the biological diversity. In this paper, in view of the environmental studies, hydraulics problems concerning groundwater were emphasized, as: • Evapotranspiration versus groundwater level corre-

lation for the Letea forest area; • The pollutant dispersion in the groundwater of the

same area; • Technical works in order to compensate the

water deficit in the soil.

2. THE INFLUENCE OF THE SURFACE WATER LEVELS ON THE GROUNDWATER FLOW IN THE LETEA PERIMETER

The hydrological Danube Delta model delivered the input data referring to the surface water levels of the surrounding free surface streams. The influence of the modification in surface water levels on the groundwater flow in the Letea perimeter was analyzed considering the following situations: Mean water levels in the surrounding free surface streams; • High water levels during the spring floods; • Low water levels during the summer drought. In table 1, the surface water levels, measured in signifi-cant sections of the hydrographic network surrounding the Letea perimeter, are presented. The surface water levels are given in absolute elevations, relative to the Black Sea level recorded at Sulina (mMNS).

Table 1 Surface water levels (mMNS)

The brook/the hydrometric station High Mean Low

Chilia branch/Periprava Station 1.03 0.73 0.56 The Magearu channel (South sandbank) 1.09 0.75 0.63

The Sulimanca brook 1.11 0.78 0.58

The influence of the surface water levels on the ground-water flow in the Letea area has been done employing mathematical modeling, using the VISUAL MODFLOW code [3, 4]. According with this code, the differential equation, which describes the three-dimensional groundwater flow, with a constant density, through a permeable medium, is:

( ) WHt

HSs ±∇∇=∂∂ K (1)

Considering the most general form, the K tensor of the hydraulic conductivity coefficients is:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=

zzzyzx

yzyyyx

xzxyxx

kkkkkkkkk

K (2)

If the coordinate axes are considered along the main flow directions, the K tensor becomes:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

zz

yy

xx

kk

k

000000

K (3)

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By definition, the hydraulic conductivity coefficient k is:

µρ gKk i= (4)

The tensor characteristic of the hydraulic conductivity is induced by the tensor feature of the intrinsic permeability, which is a property of the permeable medium, and, thus, of the porosity:

µρ gK

k ijij = (5)

Therefore, the hydraulic conductivity coefficient contains properties from both the permeable medium and the fluid (water). The MODFLOW code, from the VISUAL MODFLOW package, 3D, is developed for the scheme presented in figure 3.

Figure 3. The scheme used for finite difference model.

The extra diagonal terms of the tensors that describe the flow variables are neglected. This means that the coordinate axes are supposed to be lined up with the main flow directions. Obviously, a more complex approach is possible, in which case, the complete tensors are considered, and the calculus cell group would have 27 components. However, because the measurement data is often insufficient, only the ele-ments on the tensors’ diagonals have been considered in correspondence with the 7-cell scheme. The pressure heads H are mean values considered for the analyzed cells. In order to obtain the specific discharge vector q, Darcy’s law is applied to the pressure head H: H∇−= Kq (6)

or in detail:

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

∂∂∂∂∂∂

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

zHyHxH

kk

k

q

qq

zz

yy

xx

z

y

x

000000

(7)

The specific discharge vector q’s components are “apparent velocities”, also named “Darcy filtration velocity”. However, in the transport equation, real velocities are required (v vector), which can be obtained by dividing the apparent velocities to the value of the effective porosity, ne:

en

qv = (8)

The MODFLOW code solves equation (1) with the aid of a finite difference model, allowing the user to chose between several numerical schemes (implicit, explicit, Krank-Nicholson). The implicit type scheme is to be preferred, because it is unconditionally stable; thus not being influenced by the choice of cell dimensions or the chosen time step. A main program (MAIN) and several independent subroutines (modules) make up the general structure of the MODFLOW code. The chosen period for the numerical simulation is divided into a series of time intervals in which the boundary conditions remain constant. These intervals are also divided into time steps. The linear equation system, which results after the application of the numerical scheme, has the following general form: [ ][ ] [ ]BHA = (9)

in which: [A] = matrix of coefficients for the pressure head

in the network nodes [H] = pressure head vector [B] = free terms vector.

The equation system is formulated and solved (in order to obtain the pressure head H at the end of each time step) using iterative procedures. In the case of the Letea area, the studied domain - with a surface of about 100 square km - is limited at North and East by the Chilia branch, at South by the Magearu channel and at West, by the Sulimanca brook. This domain was divided into elements, each side measuring 500 m. The adopted mathematical model is running with boundary conditions of potential type, given by the surface water levels on the Chilia branch (at Periprava), the Magearu channel and the Sulimanca brook (table 1).

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At mean surface water levels, the hydroisohips dis-tribution indicates the flow direction from West to East, groundwater being drained by the Chilia branch (figure 4). The same direction is maintained in the case of high water levels (figure 5).

Figure 4. The groundwater flow under the influence of mean surface water levels.

On the other hand, at low water levels, the flow direc-tion is from South-South-West towards North-East, the Magearu channel supplies the phreatic aquifer from the Letea area, while the Chilia branch drains it (fig. 6).

Figure 5. The groundwater flow under the influence of high surface water levels.

Figure 6. The groundwater flow under the influence of low surface water levels.

3. THE INFLUENCE OF EVAPO-TRANSPIRATION ON THE GROUNDWATER FLOW IN THE LETEA AREA

The Letea perimeter is framed into the arid seacoast sandbank area category, where the difference between evapotranspiration and precipitation has a mean value of 400-500 mm / year. As this perimeter covers large areas, with its groundwa-ter situated at about 1 m beneath the soil surface, the aquifer being formed of uniform sand (3-10 m / day permeability), it is expected that the evapotranspiration process has a certain influence on the groundwater regime. The evapotranspiration effect was analyzed considering the surface water level regime too [5]. The mathematical model was based on the simulation of the evapotranspiration effect by withdrawing a uniform distributed discharge, according to the evapotranspiration of 120 arid days in a year. In the area of the Letea forest, the maximum effect of evapotranspiration is seen in the center of the domain, where the groundwater level diminishes with 0.43 - 0.45 m, reaching the following levels: • 0.62 mMNS from 1.05 mMNS for high waters

(figure 7); • 0.31 mMNS from 0.75 mMNS for mean waters

(figure 8); • 0.145 mMNS from 0.58 mMNS for low waters

(figure 9).

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Figure 7. The groundwater flow under the influence of evapotranspiration, at high surface water levels.

Figure 8. The groundwater flow under the influence of evapotranspiration, at mean surface water levels.

Figure 9. The groundwater flow under the influence of evapotranspiration, at low surface water levels.

4. THE POLLUTANT DISPERSION IN THE GROUNDWATER OF THE LETEA AREA

Concerning the management and the measures required for the ecological recovery of the Letea perimeter, the results of the research, regarding the evolution of pollut-ants released from surface waters and point-sources at the soil level, are presented. Also, the pollutant dispersion was analyzed considering the regime of the surrounding free surface streams. Mathematical modeling, using the VISUAL MODFLOW package, with its two components did the analysis of the pollutant evolution: MODFLOW - for establishing the groundwater velocity field, and MT3D - for pollutant dispersion. The MT3D code, using the same scheme shown in figure 3, numerically solves the transport equation [6]:

( ){

termSources

termAdvectivetermDispersive

ee CWCCntCn +∇−∇⋅∇=∂∂

3214434421qD (10)

In the general form, the dispersion tensor D has the following expression:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=

zzzyzx

yzyyyx

xzxyxx

DDDDDDDDD

D (11)

but, if the main flow directions are considered, it is reduced to a diagonal tensor:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

zz

yy

xx

DD

D

000000

D (12)

The coupling of flow modeling – conceived by MODFLOW, for a stationary regime – and pollutant transportation modeling - conceived with MT3D, for a transitory regime – was made with VISUAL MOD-FLOW (with a Windows interface). First, MODFLOW is launched, for the velocity field calculation, and then MT3D, for the computation of the mass concentration field. As a calculation hypothesis, a linear pollution source on a channel sector and, respectively, the pollution from a point source situated at the soil level was considered. The numerical results are presented as maps of the pollution front evolution in groundwater, after a 10-year period. For the Letea area case, the pollutant dispersion in groundwater was studied, as this were from a 1.5 km long linear-source appeared on the Sulimanca brook [7]. The dispersion calculation was non-dimensionally realized, considering the source with a 100 % concen-tration. At the soil level, the pollution point source

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was considered at the 6th observation shaft, the pol-lutant being copper, with a 200 ppb concentration.

Figure 10. The pollution front evolution in ground-water, due to linear and point-sources, after 10 years,

at mean water levels. Considering mean water levels of the surrounding free surface streams, the pollution front evolution after a 10-year period is represented in figure 10. It comes out that, the pollutant released from the Suli-manca brook advances along 4 km in the groundwater flow direction. For the point source, the pollution front with a concentration of 10 ppb advances along a distance of about 3 km in 10 years, in the same groundwater flow direction.

5. CONCLUSIONS

• The groundwater flow in the Letea forest ecosys-tem is influenced by the water levels of the surrounding free surface streams.

• The groundwater flow direction changes for the low surface water levels, in comparison with mean and high water levels of the surrounding free surface streams.

• Due to small differences among the water levels from the hydrographic network, the groundwater motion is produced at very small hydraulic gradients, which lead to low groundwater velocities, with impor-tant results on the pollutant dispersion.

• The pollution provided by linear and point sources develops over short distances; for example, and after 10 years it reaches distances of 3-4 km

from the sources. These data emphasize the reduced pollution vulnerability of the studied ecosystem.

• The phreatic water regime from the Letea area is significantly influenced by evapotranspiration, which has, as a result, the diminishing of the groundwater level up to 0.43 – 0.45 m. The effect of evapo-transpiration on the Letea forest ecosystem was not sufficiently elucidated.

• The reduction of the fresh water head may lead to the intrusion of salt water from a depth of 4-5 m and can affect the evolution of the vegetal mass. This phenomenon could not be examined in the studied area due to the lack of deeper shafts (of about more than 5 m) that would provide samples and, thus, facilitate the measurements of total chloride and salts in vegetation growth periods.

• To compensate for the evapotranspiration loss and to maintain the groundwater level at a necessary elevation which provides the ecosystem equilibrium, several technical measures and works were analyzed, but no efficient and practical solution concerning the cost / profit ratio was identified at the moment.

REFERENCES 1. Ionescu Al., Berca M. (1988) Ecologie şi protecţia

ecosistemelor, Bucureşti 2. *** - Convenţia asupra conservării vieţii sălbatice şi a mediului natural din Europa (1998), Strasbourg

3. Dimache Al. N. (2003) Contribuţii la mişcarea fluidelor eterogene prin medii permeabile, teză de doctorat, conducător ştiinţific prof. Virgil Petrescu, Universitatea Tehnică de Construcţii Bucureşti

4. Sîrbu N. (2002) Analiza hidrodinamicii mediilor poroase cu ajutorul elementelor finite mixte hibride, teză de doctorat, Universitatea Tehnică de Construcţii Bucureşti

5. *** - Analiza stării ecologice actuale a eco-sistemelor forestiere cu protecţie integrală Pădurea Letea şi Pădurea Caraorman din Rezervaţia Biologică Delta Dunării (2003), studiul A7/2003, faza I, Institutul Naţional de Cercetare – Dezvoltare „Delta Dunării”, Tulcea

6. Bear J., Verruijt A. (1988) Modeling Groundwater Flow and Pollution, Reidel Publishing Company

7. Dimache Gh.D. (2003) Modelarea curgerii apelor subterane, din studiul A7/2003, faza a III-a, Institutul Naţional de Cercetare – Dezvoltare „Delta Dunării”, Tulcea