The impact of the embankment and the recreational lake on capturing front with drilling wells

This paper presents the influence on the levels from the well caption front Gherăeşti-Bacău, located on the right side of the Bistrița River, through the construction, on the right shore, of a 2.25 km long perimetral embankment, and a recreational lake with a surface of 3.18 hectares and average depth of 5.5 m (Figure 1). Through numerical modelling, using the modelling software of Visual Modflow aquifer, the influence on the hydrostatic level from drilled wells was determined, as well as the influence on the phreatic flow through the making of the recreational lake, which captures a part of the underground water. The use of the mathematical model allows the determination of the optimal parameters for an extraction from the aquifer known through classical methods. To achieve the mathematical model the method of filtration resistances was used, which is applied in the case of a sudden curvature of the streamlines (in the proximity of the imperfect permeable/impervious borders: channels, drains, well systems, screens), hence they are applied during pressure/level drops. This method allows the following equalizations: the imperfect wells can be considered as perfect; the lines of perfect/imperfect wells can be considered as perfect trenches (channels) with a flow equal to the sum of all wells; a stratified aquifer (up to 3 layers) can be equivaled with a homogenous one. Aspects regarding the flow were taken into consideration: with a free level or under pressure, the dimensioning of the model, the initial conditions of the aquifer layer, the lithostratigraphic characteristics, homogeneity, anisotropy, the transfer mechanisms in the domain’s interior, the studied hydrogeological structure was schematized, having done a monolayer model. The calibration of the model consists of adjusting, in reasonable conditions, of the domain data (the permeabilities), boundary conditions, so that through the running of the model and obtaining the corresponding piezometric lines and the obtained data will overlap the levels of the existing drillings.


Case study. The Gherăești-Bacău catchment front
The Gherăești-Bacău catchment front has 57 boreholes, 8 executed in 1966 and 49 executed in 1982 (Figure 1).Currently, 44 boreholes are in operation.The catchment front is located in the municipality of Bacău, on a winding alignment that follows the old bed of the Bistrița River.The boreholes are located at an average distance of approximately 75 m from the main riverbed, being capture boreholes with infiltration from the bank.The neighbourhoods of the catchment front are represented by private homes, the Bacău II reservoir, the Bistrița River bed and the offtake of UHE Bacău I.The boreholes have depths of 8.00 -12.00 m, are completed with ɸ= 324 mm (12 3/4") steel column with flared slot filters and are spaced at an average distance of 90 m from each other.The average thickness of the collector is H = 6.58 m.The total flow rate exploited from the 44 wells is 190.00 l/s, and the maximum flow rate exploited by one borehole is: Q = 6.0 l/s (0.006 m 3 /s), with an average flow Qmed = 4.31/s (0.0043 m 3 /s).where, Kxx, Kyy, and Kzz are the hydraulic conductivity values on the x, y, and z axis (m/s); h is the potentiometric head (m); W -volumetric flux (s -1 ); t -time (s); Ss -specific storage of the porous material (m -1 ).Equation (1) combines the initial conditions imposed on the model, describes the distribution of groundwater in a homogeneous and anisotropic medium and determines the main axes of the hydraulic conductivity.

The method of filtering resistances for the calculation of catchments with wells
The method of filtering resistances is applied in the case of sudden curvature of stream lines (near imperfect permeable/impermeable boundaries: channels, drains, well systems, screens etc.), so when level/pressure drops occur [4].This method allows the following equations: imperfect wells can be considered as perfect; lines of perfect/imperfect wells can be considered as perfect trenches (channels) with flow equal to the sum of all wells; a stratified aquifer (up to three layers) can be considered a homogeneous aquifer.Thus, at distances of the same order of magnitude as the thickness of the layer, the movement of underground water is predominantly horizontal -with the distribution of pressures similar to that in the case of perfect drains.
=   +   (2) where: Φ -internal/additional resistance; Φc -the resistance of the imperfect well according to order, in the case of non-stationary movement depends also on time (it is considered constant in terms of time when  =  2 • < 5 • 10 −5 ); Φx -resistance according to the character of the opening of the layer; depends on the following factors: filter construction; modification of the structure of the stream in the area before the well, with processes of erosion (suffusion), corrosion/clogging of the filter.Even at the full opening of the aquifer layer filter, when we can consider Φc = 0, the action of the resistance Φx does not decrease (it even increases) and must be considered in the calculations.
Φ can be considered implicitly in the resistance F of a perfect well by considering: (3) where:   0 -equivalent radius of a perfect well;   -radius of the imperfect well.

Identifying the calculation relations for Φ for a simple situation, a terrain with a homogeneous layer (Figure 2)
Figure 2. Filtering scheme for one-layer terrain  =  (4) The dimensionless resistance fi from a homogeneous ground corresponds to the thicknesses mi = m, mc, m1 and is equal to: =   +   (5) where: fci -the resistance due to the imperfection according to the degree of opening in a homogeneous layer, with waterproof sole and ceiling, of thickness mi, for which these resistances are determined; fxi -resistance depending on the nature of the opening in a homogeneous layer of thickness mi.The relations established for aquifers under pressure can be used to determine the resistance Φ in the upper layer of aquifers with a free level.In this case, the thickness of the stream in the upper layer m1 and the length of the filter l are averaged, with a small approximation as follows.When placing the well filter in the upper layer of the well with a non-submersible filter, at which the hydrodynamic level reaches below the length of the filter in the upper layer l0 (l < l0), For wells with a submersible filter, where the hydrodynamic level is located above the filter: When placing the filter in the bottom layer,  1 =   + 0.5 •   .In the case of systematic vertical drainage, when averaging the sizes m1, b1 and l, instead of the dislevelment Sc it is recommended to use the ascent h in the upper layer.

Identification of the relations for the calculation of the resistance 𝜋𝜋 � for terrain with a homogeneous layer
In the previous formula  ̅ is determined with equation ( 4), in which   ��� is evaluated according to the relationship (5).The solid lines for the filter placement near the top and bottom boundaries of the layer, the dotted line (Figure 2): for filters of length l< 0,5•mi, located approximately in the middle of the layer   +  2 = (0,35 … 0,65) •   .

Development of the numerical model for the phreatic aquifer in the Gherăești -Bacău area
Mathematical modelling of groundwater flow involves knowledge of the entire system of groundwater flow, geological and hydrogeological knowledge (hydraulic conductivity, transmissivity, porosity etc.) [5,6].Based on the level measurements carried out in the field, the lithological descriptions made during the construction of the boreholes of the catchment front, the hydrogeological sections through these boreholes made available by the beneficiary, it is concluded that the aquifer system presents itself as a continuous environment within its natural limits, on the entire study area.Figure 3 shows the boreholes and observation points where level measurements were made.Using them, the map of the initial piezometric surface was developed.

Figure 3. Map of the initial piezometric surface
Aspects related to the flow regime were taken into account: with free level or under pressure, model sizing, boundary geometry, boundary conditions for the aquifer water flow system, initial conditions of the aquifer layer, litho-stratigraphic characteristics, homogeneity, anisotropy, the transfer mechanisms within the domain.The studied hydro structure was schematized, developing a unilayer model.Based on the presented data, the modelling area was established and the boundary conditions were defined [7]: • Dirichlet type condition -imposed hydraulic elevation, upstream elevation being given by the 164.00 m hydroisohypses, respectively the downstream elevation corresponding to the 162.00 m hydroisohypses; • Cauchy-type conditions (potential-dependent flow) on the Bistrița river, the imposed elevations are those representing the free surface of the water in the river; • Limit type conditions in depth, given by the impermeable layer resulting from the drillings within the catchment front; • Lines of constant or variable potential, respectively streamlines, correspond from a mathematical point of view to mixed-type boundary conditions (Dirichlet, von Neuman) (Figure 4).The data can be entered interactively, with the possibility of modifying certain parameters such as, for example, permeability discretization, base elevations, layer granularity, hydraulic conductivity.The perimeter of the hydraulically significant area was included in the active area of the numerical model, the adjacent areas being eliminated.In the horizontal plane, a discretization dx = 2100 m, dy = 2100 m was used (Figure 5).In the vertical plane, a vertical discretization was used.This discretization allows the appropriate vertical placement of the modelled objects at different elevations, the different zoning of permeability as well as different thicknesses of the aquifer (Figure 8).Based on these modelling parameters, the numerical flow model and its calibration will be designed.The model is materialized through hydroisohypses, flow directions and hydraulic gradients.These parameters are overlayed on the real situation through a basic hydrogeological map.The boundary conditions were expressed from considerations regarding the schematization of the area of interest.
In the mathematical modelling of groundwater flow processes the calibration process includes the adaptation, possibly the adjustment of the input data, of the model so that the results obtained through the numerical simulation correspond to the situation in the field [8].
The calibration of the model consists in adjusting the field data (permeabilities) and the boundary conditions in reasonable ways so that by running the model and obtaining the corresponding hydroisohypses they overlap the levels from the existing boreholes (Table 1, Figure 9).According to the mathematical model, the aquifer is mainly supplied from the high area (terrace), the groundwater inflow being approximately 500 l/s, and secondary from precipitation over the entire surface with a flow rate of 125 l/s.There is also an important connection between the aquifer and the Bistrița River, which drains the aquifer with a flow rate of 370 l/s.

Conclusion
There are a multitude of models for the simulation of groundwater dynamics in the case of catchments with wells, varying from simple to complex.A realistic approach requires a good knowledge of the classic modelling structure, mainly because every groundwater modelling system must be flexible enough to be integrated into a model of the entire system.
The hydrodynamic spectra determined on the model give a complete picture of the movement of water towards the catchment fronts.Based on them, the specific flow along the catchment fronts can be determined, the main element in establishing the optimal distances between the water catchment wells and the designed recreational lake.
By running the flow model, the map of hydroisohypses and the velocity field in the study area were obtained.Furthermore, the simulation of the flow and transport model in the groundwater was carried out.
According to the mathematical model, the aquifer is mainly supplied from the high area (terrace), the inflow of underground water being considerable.There is also an important connection between the aquifer and the Bistrița River.The flow captured by the wells in the Gherăești area represents approximately 20% of the total transited flow (at a maximum flow exploited by a borehole of Q=6.0 l/s), and the location of the designed recreational lake, according to the layout plan in the study area, does not affect the water levels in the catchment area.Wen-Hsing Ciang, Kinzelbach, Processing MODFLOW, A Simulation system for modelling grounwater flow and pollution, 2005.

Figure 4 .
Figure 4. Defining the boundary of the modelled domain in the study area

Figure 5 .
Figure 5. Discretization of the studied domain The elements used to determine the land surface in the studied area are presented in figure 6, Figure 7 and Figure 8.

Figure 6 .
Figure 6.The modelled surface with the highlighted land elevations

Figure 7 .
Figure 7. 3D representation of the land surface and waterproof layer

7 Figure 8 .
Figure 8. Discretization of the model in plan, cross-section and longitudinal section

Figure 9 .
Figure 9. Calculated piezometric levels vs. measured piezometric levelsThe total error obtained was 0.051 m.Since the size of the domain is not very large, the result can be considered as a very good one.The map of piezometric surfaces resulting from the calibration process with the distribution of capture wells on the discretized domain is presented in Figure10.

Figure 10 .
Figure 10.Map of piezometric surfaces with capture wells

Figure 11 .
Figure 11.2D and 3D representation of the evolution of the piezometric elevations in the case of drilling wells in the Gherăești area

Figure 12 .
Figure 12.Map of piezometric surfaces in the case of drilling wells in the Gherăești area and the designed recreational lake . G. and A. W. Harbugh.-A modular three-dimensional finite-difference groundwater flow model.U.S. Geological Survey Techniques of Water-Resources InvestigationsBook  6, 1988.[2] [3]   x x x -Visual Modflow Pro, U.S. Geological Survey Modular Ground-water model (2007).

Table 1 .
Coordinates and measured levels of observation wells