Steady‐State Modeling of Equilibrium Distillation

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

Reactive Distillation Applied to Biodiesel Production by Esterification: Simulation Studies

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%

<b>Steady-state modeling of reactive distillation columns</b> - doi: 10.4025/actascitechnol.v34i1.9535

<p class="aresumo">An algorithm for the solution of the mathematical model featuring reactive distillation process in steady-state columns is analyzed. It has been presumed that each stage’s outlet streams in the model were in phase equilibrium conditions and that chemical kinetics was described by a reaction rate model. Within the context of the developed algorithm a procedure to solve a set of equations in a sequential form and a methodology to produce the initial estimates was defined. Broyden’s method was employed to solve the equations that model the chemical reactions. Algorithm was evaluated by study cases of 2-pentene metathesis and MTBE synthesis. The simulation results were close to results available in the literature and the proposed algorithm proved to be efficient since in both cases the convergence towards a solution was found.</p

Adsorption of Direct of Yellow ARLE Dye by Activated Carbon of Shell of Coconut Palm: Diffusional Effects on Kinetics and Equilibrium States

In this paper, the characteristics and potential removal of direct yellow ARLE (DYA) dye by using coconut palm shell-based activated carbon (CPS-AC) were assessed. Both kinetic and equilibrium experimental data were obtained from a series of DYA dye sorption experiments. All the sorption experiments were performed in closed batch system under constant temperature and stirring speed, at the predetermined pH of initial solution. The kinetic mathematical models of pseudo-first order, pseudo-second order, Elovich and intra-particle diffusion model were used in order to better interpret the adsorption kinetics phenomenon. Equilibrium data were described by applying the isotherm models of Langmuir, Freundlich, Tóth, Sips and Khan. The best description of DYA sorption equilibrium data was achieved for the Langmuir isotherm model, reaching a maximum adsorption capacity of 100 mg·g-1. Finally, the DYA dye adsorption functional groups characterizations were successfully accomplished and the results elucidated the most important groups linked with CPS-AC surface where molecular interactions could occur. Hence, the quantitative evaluation of equilibrium and kinetic experiments of adsorption process have demonstrated that the CPS-AC adsorbent was a promising high effective adsorbent and its potential can be successfully used for DYA dye removal