Elaboração de curvas residuais com o auxílio de diferenças finitas. Um estudo comparativo

Abstract

In this thesis a new methodology for the elaboration of residual curve maps using the finite difference method using the explicit Euler method is described. To create residual curve maps, the resolution of a system of differential equations coupled together with the phase equilibrium equations is necessary. The methods generally employed to solve these differential equations often involve numerical methods known as implicit methods. This type of solution requires additional computational time and is usually more complex to implement. Explicit methods appear as an alternative for solving differential equations since their implementation is usually simpler. In view of this characteristic, an explicit method based on finite difference formulas or techniques, the Euler Method, appears as an alternative to be applied to solve the system of differential equations for the elaboration of residual curve maps. The system of differential equations to be solved by the Euler Method is formed by the equation obtained from the mass balance in a simple distillation process and the T bubble equation that was transformed into a differential equation through the concept of false transient or also called pseudo transient. The use of this methodology is an unprecedented alternative for this purpose. This method was applied to the ideal n-pentane/n-hexane/ n-heptane system and to the non-ideal systems acetone/chloroform/methanol, 2- propanol/water/propylene glycol, ethyl acetate/n-hexane/acetone, ethanol/methylcyclohexane/3 methyl pentane, water/1-propanol/glycerol. The deviation of the liquid phase was determined by the NRTL, UNIQUAC and UNIFAC models and the deviation of the vapor phase was determined by the fugacity coefficient based on the Virial Equation. The results obtained by this methodology were coherent when compared with the cataloged residual curve maps and were also shown to be consistent for the elaboration of residual curve maps for non-cataloged systems. The results in terms of thermodynamic data, such as the composition of the azeotropes, detected by the residual curve maps by the methodology proposed in this work, were compared with the experimental data and the results found from the proposed method were shown to be equivalent or close to those obtained at from known methods. In the acetone/chloroform/methanol system, the relative deviation of the molar composition of the azeotropes, the acetone/chloroform binaries were 0.001/0.004, acetone/methanol 0.003/0.001 and acetone and chloroform/methanol 0.004/0.074, and for the ternary azeotrope of the relative deviation was 0.030/0.008/0.034. For the xii ethyl acetate/n-hexane/acetone system the relative deviation of the composition of the azeotrope from the n-hexane/acetone binary 0.003/0.012 and from the n-hexane / ethyl acetate binary 0.002/0.003. For the ethanol/methyl cyclohexane/3 methyl pentane system, the relative deviation in the composition of the azeotrope of the ethanol/3 methyl pentane 0.033/0.014 and of the ethanol/methyl cyclohexane 0.000/0.000. For the water/1-propanol/glycerol system the relative deviation in the composition of the water/1-propanol binary 0.017/0.023. For the ethanol/water/glycerol system, the relative deviation of the feed composition was 0.000 for ethanol and 0.000 for water. The implementation of the Euler Method to elaborate the residual curves maps was carried out in MATLAB and the code name is residual_curves.