Modelagem híbrida do processo de troca iônica em colunas de leito fixo

Abstract

Ion exchange is a process that is used in the treatment of aqueous industrial effluents containing organic compounds and heavy metals. The fixed bed columns are longer applied by allowing the process to occur continuously (cycles of regeneration). The design and process optimization of the ion exchange column requires the use of mathematical models. Phenomenological models of these systems involve the solution of partial differential and algebraic equations. The equilibrium data for ion exchange processes are usually described by the Mass Action Law (MAL), which can be considered non-ideality of aqueous and solid phases. Artificial Neural Networks (ANN) are being used successfully for the study of equilibrium data because they are empirical models and don t demand a mathematical rigor. This work aimed to evaluate the applicability of the hybrid model to describe the dynamics of ion exchange in fixed beds of binary systems. This system consists of partial differential equations obtained from mass balance in fluid phases in the ion exchanger and ANN to describe the balance. LAM was adjusted to experimental data of ion exchange equilibrium and then were generated 4200 data sets for each binary pair studied, which served as training for RNA. We tested networks with different structures, with one and two input layers. The 3-3-2 structure was used in the simulations of the hybrid model because it was the best represented the systems during the training phase. The differential equations were solved by the lines method. A computer program in FORTRAN language was developed for solving the model equations. DASSL subroutine was used to solve the equations. The performance of the hybrid model was evaluated from the results obtained with the phenomenological model, in which case the equilibrium description was made with the use of MAL. It also was the analysis of results from the comparison of experimental data. To evaluate the model we used data from the literature of ion exchange in Amberlite IR 120 resin on the systems Cu-Na and Zn-Na and in NaY zeolite on Fe-Na and Zn-Na. Both models were efficient to describe the dynamics of ion-exchange fixed bed columns, and the hybrid model had the advantage of the reduced computational time (82% reduction on average) as a result of not needing to solve a nonlinear equation.