Mathematical Model to Predict the Salt Conditions in the Pereira de Miranda Reservoir- State of Ceara-Brazil.

Transcription

1 Mathematical Model to Predict the Salt Conditions in the Pereira de Miranda Reservoir- State of Ceara-Brazil. Souza, Raimundo Pétalas, Zoi Departamento de Engenharia Hidráulica e Ambiental Centro de Tecnologia - UCF Campus do Pici, P. O. Box , Fortaleza Ceará Cornell University School of Civil and Environmental Engineering 466 Hollister Hall Ithaca, NY, rs237@cornell.edu Abstract The Salinity Process, that occurs, with frequency, in some Superficial Reservoirs of Northeast of Brazil, motivated by the climatic variability, presents in that region, has been studied with great interest, by scientists and engineering that are worried about the water quality aspects of these bodies of water. With those goals, a lot of methods of studying have been applied, in order to get a better understood of the phenomenon. This research has as principal objective to develop a mathematical model, with base in Mass Balance Principle of a Watershed, so that it could be able to predict the evolution of the dissolved salt concentrations in the Pereira de Miranda Reservoir, at the State of Ceará - Brazil, as a function of time. The results showed that the salt concentrations are very sensitive to the behavior of the hydrologic parameters of the watershed. The results showed yet that the salt level presents in that body of water point out to the necessity of a process of monitoring, as the process of prevention. Introduction The presence of the intensity of climatic changes, around the world, has provocated deeper impacts in the environmental, particularly in the water resources. In regions where these natural resources are so scarce, as it is occurring in the Northeast of Brazil, these climatic changes can play a very important task in the amount of water available for the multiple use. In such way, it is very important the development of research programs that can bring a better understanding of the impacts caused in water quality of reservoirs, in the presence of this climatic changes. Among the principal impacts concerning with the reservoir water quality, at the Northeast of Brazil, one that needs some attention is the Salinity Process. This phenomenum, frequenty in most reservoirs of that region, has been studied for scientists and technicist that are worried with the water quality of those reservoirs. 1

2 This research has as principal objective to develop a simple methodology in order to get a better understanding about the Salinity Process, in this body of water, relating with some hydrologic parameters, like Precipitation and Evaporation, of some watershed. The relation of those parameters is studied through a Mathematical Model that can describe the balance of mass of the Reservoir Pereira de Miranda, and, in such way, to establish the behaviour of Salt Concentration, present in that system. The Mathematical Model, that considers the reservoir well mixed, and is based on the Mass Balance applied to this reservoir, permits to make an analysis of the concentration of some chemical components that are, frequently, responsible for the Salinity Process. The results found, through the Mathematical Simulation, have shown that the high level of evaporation rates, presents in that region, have performed a great influence on the incriasing of the Salt Concentration in that Reservoir. Many researchs have been studied this Reservoir in order to find the real level of Salt Concentration. They have given important cotribution about this subject. Santiago (1984) using Isotopic Models, to analyse the mechanism of the balance of mass in reservoirs, found that the Aerosols, present in the soil of that region, could be the principal source of salt, responsible for the incriasing level of Salt Concentration, at that region. Frischkorn at alli. (1980), through the same hidrochemical measument, realized in the South of Ceara, found that the old water present in the deeper aquifers of that region, apresents the high level of salt concentration, showing that the dissolution in the aquifer represents a significative contribution to the high Salt Concentration of this region. Barros (1994), studying the Reservoir Pereira de Miranda and others reservoirs, has shown that one of most important source of salt, that happened at that region, is the Aerosols that come from the Ocean through the wind in the rainfall seasons. Mathematical Model The Mathematical Model developed to study the Salinity Process in reservoir, was based in the model proposed by Crowe(1993), which has the capacity of analysis the evolution of Salt Concentration with time, as function of the climatic change of some region, and the hydrologic parameters of that watershed. In such way, this Mathematical Model, based in the Mass Balance, permits to analysis the dissolved salt concentration, in the reservoir, as it permits to establish the variation of salt concentrarion with time. To do so, the model utilizes a set of hydrologic parameter, from the same watershed where one can find the reservoir. These parameters are, basicly, Precipitation, Evaporation, Runoff and Infiltration rates. In order to relating all of those hydrologic parameters, the Mass Balance has been applied in the Control Volume, consisting by the Pereira de Miranda Reservoir, at Northeast Brazil, having as the result the following equation, 2

3 S = VP + ES - EV - VAI - R (1) where S is the rate of volume of water inside of the reservoir; VP is the volume precipited directly to the surface of the reservoir; ES is volume of water that comes to the reservoir through the runoff; EV is the volume that is evaporated from the reservoir; VAI is the volume of water that infiltrates; R is the volume of water that comes out from the reservoir, for the multiple purpose. In order to improve the computational solution of the Model, the equation (1) was putting in the form as follow, S(I) = VR(I0) + VP(I) + ES(I) - EV(I) -VAI(I) - R(I) (2) where S is the volume of water in the reservoir, in the end of the month I; VR is the volume of water in the reservoir, in the end of the last month before I 0. Therefore, through the equation (2), the program calculates the volume of water in the reservoir, each month of the year. After that, these values are used to establish the variation of the Concentrarion of Salt dissolved, in the form of ions, through the equation, C = (C v VR + C p VP + C e ES - C i VAI - C v R)/S (3) where C is the corresponding concentration of the chemical compenent, at the present month; Cv is the concentration of the chemical component in the last month; C p is concentration of the chemical component in the evaporation rate; Ci is the concentration of the chemical component in the infiltration; Ce is the concentration of the chemical component that comes into the reservoir in the form of runoff. In such way, through the equation (3), the concentration of each chemical component, that is dissolved in the reservoir, can be calculated. To do so, it is important to transform the equation (3) into the computational equation of the form, C(I,J) = ( C(I 0,J)VR(I 0 ) + C p (I,J)VP(I) + C e (I,J)ES(I,J) - C i (I,J)VAI(I) - C(I 0,J)R(I) ) / S(I) (4) where I represents the chemical component and J represents the month that the concentration needs to be calculated. 3

4 Analysis of the Results This model was applied in the Pereira de Miranda Reservoir, with the objective to measures its efficience, knowing that such reservoir is located in a semi-arid region, where the climatic variability plays a very important role in the hydrologic balance of that region. In order to simulate the Salinity Process, it is important to have the characteristic of the reservoir that will be studied. Therefore, the area of the surface water of the reservoir is 56,8 km 2 ; the relation between the area of the surface water and the area of the watershed is 0.002; the relation between the amount of water, in the reservoir, and the area of the watershed is 139 mm; and the amount of water, in the reservoir, and the area of the surface of water of the reservoir is 6,9 m. With these data, and the data of Precipitation, Evaporation and Infiltration rates, together with the inflow and outflow directly from the Reservoir, it is possible, through the Mathematical Model, to establish the temporal variation of the Concentrations of the various chemical components that are responsible to the Salinity Process. The principal chemical elements, in form os ions, that could be found, with frequency, in that reservoir, and that have been studied in this research were Calcium, Magnesium, Sodium, Potassium, Chlorine, Dissulfates, and Bicarbonates. The figure 1 shows the variation of volume of the water in the reservoir, in the period from 1980 through There one can observe that, in that period, there was a decreasing in the volume of water available in the Reservoir. This scene permits to conclude that this period could be charaterized as a dry period. This fact induces to the conclusion that, in that period, the decreasing of the volume of water in the reservoir Pereira de Miranda, has produced a damage in the behaviour of water quality with respect to the salinity, showing, in such way, that exist the necessity of the development of a severe program of management to operate this reservoir, including the water quality aspects. Figure 1 Variation of the volume of water in the Reservoir ( hm 3 ). 4

5 The figure 2 shows the concentration of various chemical components presents in the reservoir. There it can be seen that all the concentrations have a mean rate of variation positive, in the period of study, showing, in such way, that all concentrations become high at the critical period of dry season. The results show yet that the presence of chemical components, chlorine, sodium and bicarbonates have concentration higher that the others chemical components. With this, one can conclude that the risk of salinization becomes high in the periods of dry season. Figure 2 Variation of the concentration of the chemical components (mg/l). The figure 3 shows the temporal variation of the chemical conductivity of that body of water, in that period of observation. There one can see that this parameter has a positive variation rate, fact that confirms the tendency of the other results. The results of the simulation shows yet that only in the period from Feb 1984 through May 1984, there was a different tendency from the others preview discussed. This fact is justified by the tendency of the intensity of the precipitation, that has occurred in that period. Finally the figure 4 shows the behaviour of SAR Sodium Adsorption Ratios, important parameter that indicates the level of salinity, and is extremely utilized in the agricultural activities. This parameter has the principal objective to establish the risk of the permanence of Sodium in environment. Through the figure it is possible to observe that, with the conditions of this research, the SAR has the values between 3.4 and 2.6. These results permit to conclude that this parameter is extremily sensitive to the climatic changes, when this occurred in region with the same characteristic as that one found in the semi-arid of Northeast of Brazil. In the special situation of the Pereira de Miranda Reservoir, the simulation shows that the water from that reservoir is in good conditions to the irrigation use. However, it is important to note that a program of monitoring should be established, in order to observe the behariour of the reservoir with respect to salinity process. 5

6 Figure 3. Variation of the Eletrical Conductivite in the period of observation. Fig. 4. Variation of the SAR in the period of observation. Conclusions After analysis of the results, that came from the Mathematical Simulations, one can conclude that: The Mathematical Model used to simulate the Salinity Process in the Reservoir Pereira de Miranda has produced satisfactory results. However, to a better analysis, it is necessary a more complete set of hydrologic data which, certainly, will permit that the model can be capable to produce a more expressive results. 6

7 The simulation permits to conclude that the water from that reservoir has a good quality with respect to the salinity, but it is quite vulnerable to the climatic changes that happens in that region. The results have showed that there is risk of salinization, if long period of dry season occurs, without an adequate planning of users of that water. References Barros, F. F., 1994, Estudo da Qualidade de Água e Balanço de Sais em Reservatórios Superficiais na Bacia do Rio Curu. Thesis of Master - UFC, 78 pp. Crowe, A.S., 1993, The application of a coupled water-balance-model to evaluate the sensitivity of a lake dominated by groundwater to climatic variability, J. of Hydrology, 141, pp Crowe, A. S., & Schwartz, F. W., 1983, Simulation of lake watershed system II, Appication to Baptiste Lake, Alberta, Canada. J. of Hydrology 52, pp Frischkorn, H, at alli., 1988, Dados Isotópicos e Hidroquímicos da porção oriental da Bacia Potiguar. 5º Congresso Brasileiro de Águas Subterraneas, September Petalas, Z.V., 1995, Estudos de Salinização de Águas Armazenadas em Reservatórios Superficiais, Thesis of Master submited to the Department of Environmental and Hydraulic Engineering, University of Ceará. Santiago, M.M.F., 1984, Mecanismo de Salinização em Regions Semi-Áridas. Estudo dos Açudes Pereira de Miranda e Caxitoré, no Ceará. Tucci, C.E.M., 1993, Hidrologia: Ciencia e Aplicação, Coleção ABRH, vol. 4. Ward. R.C., 1967, Principles of Hydrology. Mc Graw Hill, Engleand. The author would like to thank to the Government of Brazil that, through the CAPES, has supported His sabbatical license at the Cornell University. 7