Vilmar Steffen

By Vilmar Steffen and Edson Antonio da Silva

In this chapter, an algorithm for the solution of the mathematical model featuring steady‐state multicomponent distillation columns is analyzed and applied in the case study of the separation of hydrocarbon mixture. The development of the model has assumed each stage outlet streams in thermodynamic equilibrium in the phases liquid and vapor. The modeling of liquid was considerate and the non‐ideality behavior was described by activity. The non‐ideality of gas phase was calculated by Peng‐Robinson equation of state. The model consists of a set of nonlinear algebraic equations. The algorithm and numerical procedure to solve a set of equations are presented in a sequential, general and very simple form. A methodology to produce the good initial guess was defined based on rude simplifications of the system. In the study case, the initial estimates generated by the method are very good, being only about 20% far from the simulation results and considering a tolerance of 10−10, the convergence was obtained with 28 iterations.

Part of the book: Distillation

By Vilmar Steffen

Part of the book: Distillation

By Guilherme Machado, Marcelo Castier, Monique dos Santos, Fábio Nishiyama, Donato Aranda, Lúcio Cardozo-Filho, Vladimir Cabral and Vilmar Steffen

Reactive distillation is an operation that combines chemical reaction and separation in a single equipment, presenting various technical and economic benefits. In this chapter, an introduction to the reactive distillation process applied to the biodiesel industry was developed and complemented by case studies regarding the production of biodiesel through esterification a low-cost acid feedstock (corn distillers oil) and valorization of by-products (glycerol) through ketalization. The kinetic parameters of both reactions were estimated with an algorithm that performs the minimization of the quadratic differences between experimental and calculated data through a Nelder-Mead simplex method. A 4th order Runge Kutta method was employed to integrate the conversion or concentration equations used to describe the kinetics of the reactions in a batch reactor. Both processes were simulated in the commercial software Aspen Plus with the estimated kinetic parameters. The results obtained are promising and indicate that the productivity of both processes can be improved with the application of reactive distillation technologies. The simulated esterification process with an optimized column resulted in a fatty acids conversion increase of 84% in comparison to the values lower than 50% obtained in the experimental tests. Solketal production through ketalization also achieved a high glycerol conversion superior to 98%.

Part of the book: Distillation Processes

By Vilmar Steffen, Maiquiel Schmidt de Oliveira and Edson Antonio da Silva

Reactive distillation has already been extensively studied, many applications have been evaluated by simulation and laboratory experiments, and many modifications in the configuration of the column are being proposed, such as the reactive dividing wall column. The steady state plays a key role because it is required to operate a process steadily at the optimal point, and it is necessary to use control strategies to keep the operation at this point. Thus, this chapter presents a systematic literature review, about the modeling and simulation of reactive distillation in steady state presenting some bibliometric results. It also presented some content related to the variations in the configurations of a reactive distillation column, mathematical modeling of the process, and computational simulation. Lately, simulation studies reported in the literature about this subject have mainly used sequential modular simulators like Aspen Plus. But, the solution process of the model’s equations still can be improved. Some opportunities are pointed out, like the use of heuristic algorithms for the solutions of the mathematical equations, better initial guess algorithm for the unknowns, and the use of a more generic scheme for representation of the mathematical model of a reactive distillation stage.

Part of the book: Solvents [Working title]