Calibração da dispersividade longitudinal de aquíferos através do método iterativo do gradiente de concentração

Abstract

The understanding of how the transport of solutes in ground water occurs is critical to the proper management of this resource increasingly subjected to thropogenic pressures. In order to model this process, a key parameter is the coefficient of hydrodynamic dispersion, whose most important component in porous environments is the longitudinal dispersivity (αL). The determination of αL usually takes place through experiments restricted to areas of interest and with often inaccurate results. Numerical methods are also used in order to attain parameter estimation. This study aimed mainly at calibrating αL in aquifers through the Iterative Method of the Gradient of Concentration (IMGC) derived from an adaptation of the methodology proposed for the Iterative Method of Hydraulic Gradient (IMHG). The process starts from the hydrodynamic simulation. Later, concentrations obtained from fields or in a hypothetic way are inserted using the model of simulation of solute transportation. Then, a matrix of concentrations is generated, which will work as the basis for the iterative process of IMGC. Two models were structured: one called observed or fixed model in which the concentration field is fixed and another model named calculated or not fixed. Throughout the calibration process arrays of concentrations are generated and used for calculating the spatial concentration of gradients in fixed and not fixed models. The average angle between the gradients of observed and calculated concentrations and the mean squared error are the convergence criteria to assess the calibration process. In the five models presented in this research, the results for these two criteria indicate the efficiency of the calibration method. Following the classical methodology of parameter calibration in the IMGC iterations continue as the minimum values for these criteria are not attained, therefore, the change of the longitudinal dispersivity varies among iterations. This mechanism is based on the ratio between the observed and calculated gradients of concentrations at each model cells. The results were obtained from the use of nitrate concentrations at two hypothetical samples with different degrees of complexity and also with a real case applied int he municipality of Crato, inserted in the Sedimentary Basin region of Araripe. For the cases analyzed in this study, there was a significant decay of the average angle formed between the gradients of observed and calculated concentration and the mean squared error of concentrations, obtaining as a result, a matrix with αL values close to those initially stipulated. IMGC presents itself as a practical method. It is suggested the development of a computer program that automates IMGC so that it is better used in more complex situation.