Inversão numérica de funções na determinação de pontos críticos de misturas

• Autor(a) principal: Parajara, Caroline Nascimento
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13718
• topic: Critical point of mixtures; Systems of nonlinear algebraic equations; Inversion of functions from the plane to the plane; Critical curve; Ponto crítico de misturas; Sistema de equações algébricas não lineares; Inversão de funções do plano no plano; Curva crítica; Teoria do ponto critico (Analise matemática); Misturas (Quimica); Equilíbrio líquido-vapor; Regra das fases; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

A vapor-liquid critical point of a mixture can be understood as the point where the properties of the liquid and vapor phases, such as density, viscosity, composition, molar entropy among others, converge, namely, they are identical. The occurrence of a vapor-liquid critical point of a mixture is given under specific conditions of temperature, volume and pressure of the system, specifying yet the composition of the mixture. The prediction of liquid-vapor critical point of mixtures is a challenging assignment in view of the high non-linearity of the available thermodynamic models, therefore, in this work, we proposed a new approach to the problem of vapor-liquid critical point calculation, based on the formulation of Heidemann and Khalil, and using the Peng-Robinson equation of state together with the van der Waals mixing rules. The problem can be modeled by a 2 X 2 system of nonlinear algebraic equations, which makes possible the prediction of critical points of the mixture through an adaptation of the technique of inversion of functions from the plane to the plane of Malta, Saldanha e Tomei (1993). The Euler-Newton continuation method was used in two of the three steps of the method of inversion from the plane to the plane in order that the critical points of the mixtures were obtained with more precision. We were obtained critical points from two mixtures: one having only one critical point for the given molar composition and the other having two critical points. All methods were implemented and executed in the Java programming language, version 1.8.0 and the results were compared to other published works and with the results obtained by the methods of Heidemann e Khalil (1980) and Dimitrakopoulos, Jia e Li (2014). The proposed methodology proved to be robust in the prediction of critical pointsin addition, it was able to provide a global view of the nonlinear engineering problem, where intrinsic characteristics of the models can affect the convergence of classical numerical methods, that is, the method of inversion of functions from plane to the plane is not limited only to the calculation of the solutions of the studied system like many other techniques but still offers information about the problem that supports the possibility of performing a qualitative analysis of the function to be solved.