Scientific Bulletin of the The 6th International Conference on Politehnica University of Timisoara Hydraulic Machinery and Hydrodynamics Transactions on Mechanics Special issue Timisoara, , October 21 - 22, 2004

GROUDWATER HYDRAULICS APPLIED TO THE LETEA FOREST ECOSYSTEM FROM THE DELTA

Virgil PETRESCU*, Professor, Ph.D., Alexandru DIMACHE, Lecturer, Ph.D., Hydraulics and Environmental Protection Hydraulics and Environmental Protection Department, Technical University of Department, Technical University of Civil Engineering Bucharest 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: [email protected]

ABSTRACT The Letea forest ecosystem, situated in the Danube q [m/s] specific discharge vector (on the unit Delta Biosphere Reservation, between the Chilia and surface) Sulina branches, has imposed, within the framework v [m/s] velocity vector 3 of the ecological recovery, the carrying out of certain C [kg/m ] mass concentration 3 research activities concerning the current state of the Cs [kg/m ] mass concentration at the source environment, and, respectively, the interdependency ne [-] effective porosity 2 of the surface and groundwater regime, climatic, D [m /s] dispersion tensor (of the hydrodynamic pollution control, relief and soil conditions, in accor- dispersion coefficients). dance with the 2000 /60 / CE Frame Directive (“The action framework in the water policy domain”). 1. INTRODUCTION The Letea forest from the (figure 1) has KEYWORDS an overall surface of 5,396 ha, out of which the integral protected area is of about 2,800 ha (figure 2). It has Forest ecosystem, groundwater, mathematical model, been under protection since 1930 (together with the pollutant dispersion, evapotranspiration process. Caraorman forest), and since 1938 it has been declared a natural reservation. The Letea forest has been included NOMENCLATURE in the international UNESCO biosphere reservations th Ss [1/m] specific storage coefficient network at the 4 Session of the International Council H [m] pressure head for the Coordination of the Man and Biosphere Program K [m/s] tensor of the hydraulic conductivity (MAB), Paris, November 1979. Only research and coefficients documentation activities are allowed inside the integral kxx, kyy, kzz [m/s] components of the hydraulic protected area, while keeping in focus the uniqueness conductivity coefficients along the coordinate of the forest ecosystem, with century old oak, poplar axes x, y, z, respectively and ash trees raised on fluvial-maritime sandy islands 2 Ki [m ] intrinsic permeability coefficient having phreatic water at the soil surface or near by, t [s] time and with more than 100 mammal, bird, reptile, amphib- W [1/s] flow sources related to the unit volume ian and invertebrate protected species [1, 2]. (water withdrawal and/or injection) As a result of the execution of several hydro technical 3 ρ [kg/m ] water density works in the vicinity of the protected area, works done g [m/s2] gravitational acceleration considering other purposes (flood protection for the µ [kg/(ms)] dynamic viscosity coefficient for water 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 2. THE INFLUENCE OF THE SURFACE from the influence of the natural Danube’s flooding WATER LEVELS ON THE GROUNDWATER regime. Thus, the cut-off from the natural soil regen- FLOW IN THE LETEA PERIMETER eration by the Danube’s alluvia and the salt concen- The hydrological Danube Delta model delivered tration increase in the soil, due to the evapotranspiration the input data referring to the surface water levels of (800 mm / year) being greater than precipitation (320 the surrounding free surface streams. mm / year), occur. These are phenomena, which may constitute limiting factors of the biological diversity. The influence of the modification in surface water levels on the groundwater flow in the Letea perimeter was In this paper, in view of the environmental studies, analyzed considering the following situations: hydraulics problems concerning groundwater were emphasized, as: Mean water levels in the surrounding free surface • Evapotranspiration versus groundwater level corre- streams; lation for the Letea forest area; • High water levels during the spring floods; • The pollutant dispersion in the groundwater of the • Low water levels during the summer drought. same area; In table 1, the surface water levels, measured in signifi- • Technical works in order to compensate the cant sections of the hydrographic network surrounding water deficit in the soil. 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 /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 ⎡kxx kxy kxz ⎤ ⎢ ⎥ mathematical modeling, using the VISUAL K = ⎢k yx k yy k yz ⎥ (2) MODFLOW code [3, 4]. According with this code, ⎢k k k ⎥ the differential equation, which describes the three- ⎣ zx zy zz ⎦ dimensional groundwater flow, with a constant density, If the coordinate axes are considered along the main through a permeable medium, is: flow directions, the K tensor becomes: ∂H S = ∇()K ∇H ±W (1) ⎡kxx 0 0 ⎤ s ∂t ⎢ ⎥ K = 0 k 0 (3) ⎢ yy ⎥ Considering the most general form, the K tensor of the ⎢ 0 0 k ⎥ hydraulic conductivity coefficients is: ⎣ zz ⎦

714 By definition, the hydraulic conductivity coefficient ⎡∂H ⎤ k is: ⎢ ⎥ ⎡q ⎤ ⎡k 0 0 ⎤ ⎢ ∂x ⎥ Ki ρ g x xx k = (4) ⎢ ⎥ ⎢ ⎥ ⎢∂H ⎥ µ q = − 0 k 0 (7) ⎢ y ⎥ ⎢ yy ⎥ ⎢ ∂y ⎥ ⎢ ⎥ The tensor characteristic of the hydraulic conductivity q ⎢ 0 0 kzz ⎥ ⎢ ⎥ ⎣ z ⎦ ⎣ ⎦ ∂H is induced by the tensor feature of the intrinsic ⎢ ⎥ permeability, which is a property of the permeable ⎣⎢ ∂z ⎦⎥ medium, and, thus, of the porosity: The specific discharge vector q’s components are

Kij ρ g “apparent velocities”, also named “Darcy filtration k = (5) ij µ velocity”. However, in the transport equation, real velocities are required (v vector), which can be Therefore, the hydraulic conductivity coefficient obtained by dividing the apparent velocities to the contains properties from both the permeable medium value of the effective porosity, ne: and the fluid (water). q The MODFLOW code, from the VISUAL MODFLOW v = (8) n package, 3D, is developed for the scheme presented in e figure 3. 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: [A][H ][]= B (9)

Figure 3. The scheme used for finite difference model. in which: [A] = matrix of coefficients for the pressure head The extra diagonal terms of the tensors that describe in the network nodes the flow variables are neglected. This means that the [H] = pressure head vector coordinate axes are supposed to be lined up with the [B] = free terms vector. main flow directions. Obviously, a more complex approach is possible, in which case, the complete The equation system is formulated and solved (in order tensors are considered, and the calculus cell group to obtain the pressure head H at the end of each time would have 27 components. However, because the step) using iterative procedures. measurement data is often insufficient, only the ele- In the case of the Letea area, the studied domain - ments on the tensors’ diagonals have been considered with a surface of about 100 square km - is limited at in correspondence with the 7-cell scheme. North and East by the Chilia branch, at South by the The pressure heads H are mean values considered Magearu channel and at West, by the Sulimanca for the analyzed cells. brook. This domain was divided into elements, each In order to obtain the specific discharge vector q, side measuring 500 m. The adopted mathematical Darcy’s law is applied to the pressure head H: model is running with boundary conditions of potential type, given by the surface water levels on the Chilia q = −K ∇H (6) branch (at Periprava), the Magearu channel and the or in detail: Sulimanca brook (table 1).

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

3. THE INFLUENCE OF EVAPO-TRANSPIRATION Figure 4. The groundwater flow under the influence ON THE GROUNDWATER FLOW IN THE of mean surface water levels. LETEA AREA

On the other hand, at low water levels, the flow direc- The Letea perimeter is framed into the arid seacoast tion is from South-South-West towards North-East, the sandbank area category, where the difference between Magearu channel supplies the phreatic aquifer from evapotranspiration and precipitation has a mean the Letea area, while the Chilia branch drains it (fig. 6). 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); Figure 5. The groundwater flow under the influence • 0.145 mMNS from 0.58 mMNS for low waters of high surface water levels. (figure 9).

716 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 7. The groundwater flow under the influence figure 3, numerically solves the transport equation [6]: of evapotranspiration, at high surface water levels. ∂C n = ∇ ⋅()n D∇C − q∇C + W C (10) e ∂t 1424e 434 123 {s Dispersive term Advective term Source term In the general form, the dispersion tensor D has the following expression:

⎡Dxx Dxy Dxz ⎤ ⎢ ⎥ D = ⎢Dyx Dyy Dyz ⎥ (11) ⎢ ⎥ ⎣Dzx Dzy Dzz ⎦ but, if the main flow directions are considered, it is reduced to a diagonal tensor:

⎡Dxx 0 0 ⎤ ⎢ ⎥ D = 0 D 0 (12) ⎢ yy ⎥ ⎣⎢ 0 0 Dzz ⎦⎥ The coupling of flow modeling – conceived by Figure 8. The groundwater flow under the influence MODFLOW, for a stationary regime – and pollutant of evapotranspiration, at mean surface water levels. 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- Figure 9. The groundwater flow under the influence tration. At the soil level, the pollution point source of evapotranspiration, at low surface water levels.

717 was considered at the 6th observation shaft, the pol- from the sources. These data emphasize the reduced lutant being copper, with a 200 ppb concentration. 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 Figure 10. The pollution front evolution in ground- the cost / profit ratio was identified at the water, due to linear and point-sources, after 10 years, moment. at mean water levels. REFERENCES Considering mean water levels of the surrounding free surface streams, the pollution front evolution 1. Ionescu Al., Berca M. (1988) Ecologie şi protecţia after a 10-year period is represented in figure 10. It ecosistemelor, Bucureşti comes out that, the pollutant released from the Suli- 2. *** - Convenţia asupra conservării vieţii sălbatice manca brook advances along 4 km in the groundwater şi a mediului natural din Europa (1998), Strasbourg flow direction. For the point source, the pollution 3. Dimache Al. N. (2003) Contribuţii la mişcarea front with a concentration of 10 ppb advances along fluidelor eterogene prin medii permeabile, teză de a distance of about 3 km in 10 years, in the same doctorat, conducător ştiinţific prof. Virgil Petrescu, groundwater flow direction. Universitatea Tehnică de Construcţii Bucureşti 4. Sîrbu N. (2002) Analiza hidrodinamicii mediilor 5. CONCLUSIONS poroase cu ajutorul elementelor finite mixte hibride, • The groundwater flow in the Letea forest ecosys- teză de doctorat, Universitatea Tehnică de Construcţii tem is influenced by the water levels of the Bucureşti surrounding free surface streams. 5. *** - Analiza stării ecologice actuale a eco-sistemelor • The groundwater flow direction changes for the low forestiere cu protecţie integrală Pădurea Letea surface water levels, in comparison with mean şi Pădurea Caraorman din Rezervaţia Biologică and high water levels of the surrounding free Delta Dunării (2003), studiul A7/2003, faza I, surface streams. Institutul Naţional de Cercetare – Dezvoltare „Delta • Due to small differences among the water levels from Dunării”, Tulcea the hydrographic network, the groundwater motion 6. Bear J., Verruijt A. (1988) Modeling Groundwater is produced at very small hydraulic gradients, which Flow and Pollution, Reidel Publishing Company lead to low groundwater velocities, with impor- 7. Dimache Gh.D. (2003) Modelarea curgerii apelor tant results on the pollutant dispersion. subterane, din studiul A7/2003, faza a III-a, Institutul • The pollution provided by linear and point Naţional de Cercetare – Dezvoltare „Delta Dunării”, sources develops over short distances; for example, Tulcea and after 10 years it reaches distances of 3-4 km

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