Mathematical modelling of groundwater flow and pollution of Caldas da Rainha – Nazaré aquifer system
Catarina PAZ
Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal, [email protected]
Abstract: The Caldas da Rainha – Nazaré aquifer system, namely the corresponding sector to the Tifonic Valley of Caldas da Rainha, is situated in a region which the development goals include the sustainable use of groundwaters. Therefore, in this context, is very important to know the dynamics of groundwater flow in the aquifer. To do that, a mathematical model was built based on the physical characteristics of the aquifer, which permits to predict its behavior according to different scenarios. The mathematical modeling was done using the ASMWIN software and it permitted to verify the responses of the aquifer to simulations that translate the actual situation without well extraction, the actual situation with well extraction and two predicting scenarios, one simulating the increase of extraction and other simulating the injection of a contaminant on a certain point of the aquifer. Groundwater modeling made it possible to understand the importance of the aquifer/rivers dynamics, which assumes therefore a preponderant role in the plans of future development to the region.
Keywords : Aquifer, mathematical modeling, groundwater flow, well, contamination
1. Introduction
The Caldas da Rainha – Nazaré aquifer system is constituted by two separated aquifers, one corresponding to the Tifonic Valley of Nazaré and the other to the Tifonic Valley of Caldas da Rainha, which is the object of the present study. The system is included in the West Region of Portugal, an area of growing need for water and growing environmental pressure because of the development and specialization of agriculture, for example, or the intensive pig farming that is very common in the region, among other economical activities that are established or that are planned to develop in the near future. Furthermore, it is spread by five municipal administrations, which makes it a target of the consequences of different political planning. Therefore, it is very important to know how these different acting forces influence the aquifer behavior and how it can affect the quality of its waters and also the interacting with other hydrological bodies like rivers. Still, according to Almeida et al. (2000) the aquifer was sub exploited at the end of the past decade. To translate the dynamics of groundwater flow on the aquifer, and to understand how it reacts to solicitations, a model was built. This was done taking as a base the physical characterization of the aquifer.
2. Location
The aquifer is located in the west region of Portugal (Fig. 1), spreading by the five municipal administrations of Nazaré, Alcobaça, Caldas da Rainha, Óbidos and Bombarral.
Fig. 1 – Location of the aquifer in Portugal. According to the Programa Territorial do Desenvolvimento do Oeste (2008), it is a region where the general plans of development are based on specialized agriculture, namely in the production of pêra rocha (a trade mark of pear), beach and historical tourism, and golf destination also. It is also expected the increase of population living there. On the other hand there is the pig meat production that is established for many years. All these economical plans involve the use of the aquifer’s waters and can change the quality of them.
3. Physical characteristics
In order to build the model, the physical characteristics were gathered. Data was mostly collected from SNIRH, the hydrological resources information national service of Portugal.
To calculate the average annual precipitation in the study area, data from seven rainfall stations included or surrounding the study area was used. The average estimated value is 770mm / year.
Because the type of climate is mediterranic, it rains mostly during winter time. So, during summer, rivers can have a low flow or even be almost inexistent. During winter, the opposite happens. Hydrometric data relative to the rivers was collected and computed from the hydrometric stations located in the study area, namely average instantaneous hydrometic level and average summer flow (Table 1).
Table 1 – Hydrometric data relative to the rivers, in the studied area. River Average instantaneous Average summer flow (m 3/s) hydrometic level (m) Alfeizerão 0.91 - Tornada 2.89 - Arnóia - 0.32 Rial 0.23 -
About geological and hydrological setting, according to Almeida et al. (2000), in the basis of the aquifer there is a 20 to 35 m thick formation constituted by marine sands of Late Pliocene, that lays on the Dagorda Malms formation. Following there are continental sands, with beds of lignite and diatomites, also of Late Pliocene. There is sometimes the appearance of pebbles and occasionally one or more quarters of thin sandstone and limestone conglomerates. The Pliocene formations in some areas are covered by modern alluvium, namely the spot that lies between Alfeizerão and S. Martinho do Porto.
Legend M – Dagorda Malms P – Pliocene and Quaternary sands of variable granulometry J – Jurassic sandstone, clay and limestone F - Fault
Fig. 2 – Tifonic valley of Caldas da Rainha (schematic profile) (adapted from Mira, 1999).
Because of the complexity of the tectonic processes that formed the tifonic valley (Fig. 2), the geometry of the aquifer deposits that have filled it has a great variation. Statistically, it was registered an average thickness of 70 to 150 m. The aquifer is unconfined to confined, multi layer, although it was admitted in the modeling phase, for commodity, that it has just one layer.
It was also studied the distribution of hydraulic conductivities, K, based on the private wells characteristics, which were given by ARH Tejo, the Portuguese entity responsible for the aquifer management. It became evident that there are two main zones, the northern displaying the higher K and the southern displaying the lower, and differing by one order of magnitude. This was important in the mathematical model building, because it was used initially during calibration to establish the K distribution for the model.
2. Water consumption data
Data relative to the extraction rates and other characteristics of public wells was received from the municipal administration of Caldas da Rainha and Óbidos. It permitted to establish values of extraction rate later on the modeling phase ( Table 2).
About private wells, the data collected from ARH Tejo, only refers to K, location, topography (which permitted to establish the top of the model in the modeling phase), depth of the Dagorda Malms’ top (which permitted to establish the bottom of the model in the modeling phase).
Hence, the volume rate of extraction for private wells is not known. It is just known that its finality is agriculture and industry (few). Also, it is known the location of the wells that belong to the municipal administration (M. A.) of Alcobaça but it was not possible to collect that data. So, it wasn’t used on the modeling phase. In Fig. 3 is shown the location of all the wells.
Fig. 3 – Location of wells in the studied sector.
3. Piezometric analysis
To investigate if the aquifer was confined or not, a careful study of piezometry was taken. Charts of piezometry versus time relative to data registered in the seven piezometric stations in the study area, based mostly on data posterior to 2000, were plotted. Piezometry showed to be very variable seeming to relate to precipitation. So, it was studied the relation between piezometry and precipitation (Fig. 4) on one of the stations, which showed that the two are connected. This way, and to effects of modeling, the aquifer was considered non-confined.
16 300.00 14
250.00 (mm) 12 10 200.00 8 150.00 6 100.00 4 2 50.00 Piezometric level Piezometriclevel (m) 0 0.00 Monthly precipitation Monthly 86 87 88 89 90 90 92 93 86 87 89 91 92 93 94 ------Jul Set Jan Jun Fev Abr Dez Out Out Mai Ago Mai Nov Mar Mar PiezometriaPiezometry Time PrecipitaçãoMonthly precipitation mensal
Fig. 4 – Piezometry at station 326/36 and monthly precipitation versus time.
4. Mathematical modeling
4.1 Conceptual model
First it was defined a conceptual model which simplifies reality and helps to understand the behavior of the system. As it has been said, it was considered a one layer aquifer, non-confined and with a porosity of 20%. The model area is coincident with the tifonic valley of Caldas da Rainha sector, its top was considered to be coincident with topography, and its bottom was considered to be coincident with the top of the Dagorda Malms litologic layer. Boundary conditions were established according to groundwater flow through the aquifer, from East to West approximately, occurring similarly to the hydrographic net. The topography was also considered, as the groundwater flow is similar to superficial flow. The bay of S. Martinho do Porto was defined as a discharge zone being the piezometric level in that area of 0m (sea level) (see green ellipse in Fig . 5). Also, according to the hydraulic conductivity of geologic formations, since a bigger K stimulates a bigger flow (Lencastre e Franco, 1992), the Plistocenic/Jurassic contacts and alluvial zones were established as a flow boundary zone. The Malm/Jurassic contacts were defined as no flow boundaries because of the weak capacity of malms to conduct water (Ribeiro, 2008) (Fig . 5).
Fig. 5 – Boundary conditions (flow boundaries in pink, no flow in grey) and boundary zone of discharge (green ellipse) in the finite-difference grid.
The aquifer is recharged directly by precipitation or, eventually, by rivers. The recharge was assumed as 15 to 20% of the average annual precipitation (Almeida et al, 2000), 770 mm/year. The rivers considered were the Tornada, Alfeizerão and Arnóia.
Extraction was considered to be that regarding to public wells of the municipal administrations of Caldas da Rainha and Óbidos.
4.2 Mathematical model
The mathematical model was created using the ASMWIN software (Chiang et al., 1998), which uses the finite-difference technique to compute piezometric values in each cell of the finite-difference grid as function of the input values that characterize the groundwater flow.
A grid of 150×150 cells was defined, representing each cell a square of 200m×200m (Fig. 5). As said before, the type of aquifer was defined as non confined and it was also considered isotropic. All other parameters described before, such as boundary conditions, aquifer top and bottom, porosity, initial hydraulic heads (piezometric values), recharge, leakage (rivers) and hydraulic conductivities, were inserted in the modeling software in order to build the model. The modeling was done admitting that the aquifer is in balance through time i.e. the quantity of water that flows into the aquifer is approximately equal to the one that flows out of it – steady-state case.
Calibration was done without extraction being considered (no wells inserted). A set of six piezometric observation points was inserted in the model, so that the calibration could be done. These points are coincident with the real piezometric stations in the study area and each one has a hydraulic head value measured at a chosen moment in time which is used as a reference to which the hydraulic heads computed by the model will be compared. This comparison is done through scatter diagrams. To calibrate the model, the K distribution in the grid was changed until a good scatter diagram was found. Note that a good scatter diagram is the one in which the observed and calculated heads are similar.
Hydraulic conductivity was calibrated with a final map of K that can be seen in Fig. 6, and values of -3 -4 -4 K1 = 4.00×10 m/s, K2 = 6.40×10 m/s and K 3 = 7.20×10 m/s for each zone.
Fig. 6 – Calibrated distributions of K in the finite-difference grid.
Then, the leakage factor, that translates the magnitude of water changes between the rivers and the aquifer, was calibrated, with a final value of 2.5×10 -6 s-1. This was done using a null recharge and just considering the Arnóia River. The value of the leakage factor would be changed until the water balance results showed a leakage flow equal to what was measured in the hydrometric station during summer (Table 1).
The recharge was also calibrated, being varied from 15% to 20% of the average annual precipitation. As the results were very similar, the latter was chosen. The model was now ready to start the simulation phase.
4.3 Simulation with extraction
The 23 well locations and extraction rates were inserted in the model, defining two different scenarios, one that translates the present reality – scenario 0, and another one that recreates an hypothetical case of 50% raise of extracting (multiply scenario 0 by 1.5) – scenario 1. (see Table 2).
Table 2 – Well coordinates and extraction rates that were inserted in the model. Scenario 0 Scenario 1 Municipal Name of M (m) P (m) administration the well Extraction Extraction rate (m 3/s) rate (m 3/s) JK 25A 112585 270817 3.48E-02 5.23E-02 PS7 112461 270924 1.67E-02 2.50E-02 JK26 111194 275406 1.17E-02 1.76E-02 JK27 111535 276872 3.00E-02 4.49E-02 PS 9B 111119 275709 2.42E-02 3.64E-02 RA 5 111377 276628 2.78E-02 4.17E-02 RA 8 110825 275960 1.05E-02 1.57E-02 Caldas da RA 9 111122 276817 1.46E-02 2.19E-02 Rainha PS 6 111317 276332 3.55E-02 5.33E-02 RA 22 111483 275768 1.73E-02 2.60E-02 RA 11 112773 279729 5.96E-02 8.93E-02 RA 21 112837 279807 RA 14 112714 278994 3.11E-02 4.66E-02 RA 16 112848 279913 1.35E-02 2.03E-02 RA 3 108647 274147 2.08E-02 3.12E-02 RA 6 108680 274159 JK8 106318 263673 2.75E-03 4.12E-03 RA1 112419 270018 2.07E-02 3.11E-02 RA2 111960 269530 3.83E-03 5.75E-03 Óbidos RA3 112564 270106 1.92E-02 2.88E-02 RA4 112209 269760 1.92E-03 2.88E-03 RA5 111274 269681 4.07E-03 6.11E-03 RA8 111024 269508 4.00E-03 6.01E-03
The results obtained are shown in Table 3 and the iso-piezometric maps are shown in Fig. 7 and in Fig. 8.
Table 3 – Water budget results obtained to the two scenarios.
Scenario 0 Scenario 1 Flow term In Out In-Out In Out In-Out Constant Head 1.015E+02 6.033E+01 4.122E+01 1.017E+02 6.028E+01 4.140E+01 Well 0.000E+00 4.046E-01 -4.046E-01 0.000E+00 6.070E-01 -6.070E-01 Leakage 3.400E-01 4.173E+01 -4.139E+01 3.400E-01 4.170E+01 -4.136E+01 Recharge 5.733E-01 0.000E+00 5.733E-01 5.733E-01 0.000E+00 5.733E-01 Total 1.025E+02 1.025E+02 8.392E-05 1.026E+02 1.026E+02 1.450E-04
Alfeizerão River Alfeizerão River
Tornada River Tornada River
Arnóia River Arnóia River
Fig. 7 – Iso-piezometric map of scenario 0. Fig. 8 – Iso-piezometric map of scenario 1. Note:Well cells are represented in red, leakage cells that feed the aquifer in blue and leakage cells that are fed by the aquifer in green blue.
It can be seen that little change has occurred from Scenario 0 results to Scenario 1 results. In fact, the total “in-out” shows a variation from 8.392×10 -5 m3/s to 1.450×10 -4 m3/s (Table 3).
Another important thing is that the southern river, represented in blue at Fig. 7 and Fig. 8, which corresponds to the Arnóia River, is feeding the aquifer, while the other two (Tornada and Alfeizerão) are being fed by the aquifer. This has never changed during all simulations. Note that, in the water budget, the raise of extraction rate leads to less water losses from leakage, but the gain is still the same.
4.4 Simulation of contamination
To simulate the injection of a contaminant and describe contaminant transport the ASMWALK module, a tool from the ASMWIN software, was used. This module uses tracer particles to describe contaminant transport (Chiang et al., 1998).
A permanent simulation of an injection of a 1Kg mass contaminant was performed. This contaminant was constituted by 100 particles, each one with a mass of 10g. Prevision was done to a scenario of 120 days, with a 86400s step (number of seconds in one day). The injection was introduced at cell (40,42) and three hypothetical points of observation were introduced also, with grid coordinates of (41,41) to the most near to the contamination source, (44,40) to the one placed on the Tornada River and (45,38) to the Alfeizerão River (Fig. 9).
Alfeizerão River
Tornada River
Arnóia River
Fig. 9 – Location of the contamination point (green) and the observation points (black).
The concentration-time curve that resulted from this simulation can be seen in Fig. 10 and shows that the contaminant arrives to all the observation p oints, which was expected, due to their proximity to the source of contamination. It takes 5 days to arrive to the nearest point (41,41), 15 to arrive to Tornada River and 33 to arrive to the Alfeizerão River. Note that any of these points, incl uding the injection point, can be coincident with some well that is not inventoried by ARH Tejo and so it is not displayed at Fig . 3.
Fig. 10 – Concentration-time curves referring to the observation points. Note that each division on the time scale represents 10 days.
5. Conclusions
The aquifer is able to support a raise of extraction rate, according to the comparing o f results between Scenario 0 and Scenario 1. This raise can happen if the resident population of the west r egion keeps rising or if the economical plans of tourism, namely those related to golf, and agriculture go ahead.
On the other hand , the aquifer/ri ver and the aquifer/river/wells interaction is very important since the Arnóia River feeds the aquifer and the Tornada and Alfeizerão are fed by its waters. A raise of extraction rate can lead to less water being given to Tornada and Alfeizerão, which can reduce their flow rate , leading to environmental problems . Still, r elating to the results of the second simulation, contamination that reaches these two rivers will readily arrive to S. Martinho do Porto bay, reducing the water quality of that beach’s waters. Territorial vigilance and management should be done in order to avoid actions and location of structures (like landfills, oil stations, cemeteries) that can provoke contamination. Moreover, the Arnóia River, if contaminated by external sources like intensive pig farming effluents, will contaminate the aquifer waters. Still, Arnóia’s flow rate can be reduced if extraction rises too much, but this should be more carefully studied.
So, a carefully planning of future development for the region must be performed, bearing in mind that the actions of different development lines can result in the alteration of the dynamics of the aquifer groundwater flow, its interactions with the hydrographic net and the quality of their waters.
Acknowledgements The author gratefully acknowledges Serviços Municipalizados de Caldas da Rainha e Óbidos and ARH Tejo for providing information about well characteristics.
References
Almeida, C., Mendonça, J., Jesus, M., Gomes, A. (2000) Sistemas Aquíferos de Portugal Continental. Instituto da Água, Portugal.
Lencastre, A., Franco, F. (1992) Lições de Hidrologia. Universidade Nova de Lisboa, Monte da Caparica, Portugal.
Mira, J. (1999) Síntese Hidrogeológica do Concelho de Caldas da Rainha. Universidade de Évora, Évora, Portugal.
Programa Territorial do Desenvolvimento do Oeste (2008) – Report by Associação de Municípios do Oeste,Portugal.
Ribeiro, L. (2008) Águas subterrâneas – Conceitos e métodos. Textos de apoio à cadeira de Gestão Integrada de Bacias Hidrográficas. Mestrado em Engenharia do Ambiente, 2º ano, 1º semestre. Instituto Superior Técnico, Lisboa, Portugal.