Optimization and Modelling of a CSTR Reactor Using Numerical Methods

Abstract

This report deals with differential equations and how they can be used to help the chemical engineer to size and optimize a CSTR reactor. The purpose of this article is to demonstrate the behavior of an elementary reaction where A forms B, in a first order reaction, to use the numerical methods of Euler and Runge Kutta to do so and to evaluate thermodynamic parameters of the reaction. These equations relate several characteristics of a fluid and for the type of specific reaction are tested to obtain the profile of Xa, Xb and γ, these being, dimensionless, that for Xa and Xb show how A is spent and B is produced and γ serves to relate the input temperature and at a certain point in the reactor. For the stationary solution, the bisection method was used to find the γ and then Xa and Xb. To solve the differential equations, the Euler and Runge-Kutta methods of the 4th order were used. From this the profiles were evaluated, and a great "sensitivity" was verified in the equations, since any change of parameters affected drastically in the iterations of the numerical methods. However, it was possible to find values for Xa, Xb and gamma that made chemical and mathematical sense for both a theoretical and a practical example (cyclopropanepropene). It was possible to evaluate the decay and ascent profiles of reagents and products using Excel as a tool, and the differential equations proposed in this study were successfully used.