A Short Method To Calculate Residue Curve Maps in Multireactive and Multicomponent Systems

Abstract

Reactive residue curve maps (RRCMs) are useful for the design of reactive distillation columns as a tool to establish feasible zones of reaction−separation. However, the calculation of an RRCM usually involves great computational effort due to the nonlinearity of the model equations and its iterative nature for the determination of reactive phase equilibrium. In this study, a simplified method for the generation of RRCMs is presented. This method is based on the application of reaction-invariant composition variables and assumes that the phase equilibrium constants (i.e., the relative volatilities) are independent of the temperature. Specifically, the phase equilibrium constants are calculated using a suitable estimation of the bubble temperature obtained from pure-component boiling temperatures and the reaction-invariant composition of liquid phase. These assumptions avoid iterative phase equilibrium calculations for obtaining a good approximation of RRCMs. Several reactive systems are used to identify the capabilities and limitations of the proposed method.

Short-Cut Method for the Design of Reactive Distillation Columns

“…These operating conditions are commonly used in industry for these reactive mixtures. Details of the reactive systems are reported in Table 1, and all model parameters were obtained from Carrera-Rodríguez et al 3 All reactions are assumed to be reversible and in thermodynamic equilibrium. In all the cases, the heuristic of 1.1R min was used to fix the operating reflux ratio, and the column feed was assumed to be saturated liquid, saturated vapor, and liquidÀvapor mixtures with q = 0.25, 0.5, and 0.75, respectively.…”

“…Reactive residue curve maps (RRCMs) are useful for the design of RD columns as a tool to establish regions of reaction and separation. 3 A residual curve represents the change of the liquid composition as a function of time during a simple distillation. Thus, RRCMs provide the possibility of determining the existence of distillation boundaries and, as a consequence, determining different potential separation regions.…”

“…Note that, to obtain physical consistency using these transformed mole fraction variables, the criteria for selecting a feasible set of reference components include the requirements that matrix N be invertible and that the product v TOT T N À1 be a row vector containing negative or zero entries. 3 For all case studies considered in this work, the principal products (MTBE, TAME, and ETBE) were chosen as reference components because these components are able to obtain physical consistency in reactioninvariant composition space. To evaluate thermodynamic properties during the design of RD columns, the transformation procedure X f x is necessary, and the reference mole fractions can be calculated using eq 1 and the equilibrium constants for each reaction, K eq,l , by solving a system of r nonlinear equations given by…”

“…2 In particular, the use of composition variables in molar units is not suitable for modeling reactive systems because these variables do not have the same dimensionality as the number of degrees of freedom given by the Gibbs phase rule for reactive systems. 3,4 Based on this fact, some approaches for the transformation of composition variables have been introduced in the literature, 2,4 with the aim of providing a simpler thermodynamic framework for treating systems subject to chemical reactions. These approaches are generally based on transformation of the physical compositions, and their principal benefit is that the simultaneous chemical and physical equilibrium model in reactive mixtures is very similar to a strictly physical equilibrium model.…”

Diseño conceptual de un proceso de reacción-separación para la producción de biodiesel

“…Sin embargo, también se han utilizado como una herramienta de entendimiento en la destilación con reacciones químicas en equilibrio (Barbosa y Doherty, 1988) o aplicando ecuaciones de velocidad para cinéticas ficticias (Solokhin y col., 1990 a, b) o bien mediante expresiones cinéticas experimentales para reacciones catalíticas homogéneas (Venimadhavan y col., 1994) y heterogéneas (Thiel y col., 1997). No obstante, existen varias dificultades numéricas al querer modelar o diseñar un sistema de DR, las cuales tienen su origen principalmente por la naturaleza multicomponente del sistema reactivo, en particular, el uso de variables de composición en unidades molares que no son adecuadas para modelar los sistemas reactivos, debido a que estas variables no tienen la misma dimensión que el número de grados de libertad dados por la regla de fase de Gibbs para sistemas reactivos (Carrera-Rodríguez et al, 2011a;Ung and Doherty, 1995). Por esta razón se ha reportado en la literatura aproximaciones de transformación de la variable composición con la premisa de que los modelos usados para caracterizar estos sistemas de DR sean expresiones matemáticas de la misma forma que los reportados en los sistemas de destilación simple (Wasylkiewicz and Ung, 2000;Seider and Widagdo, 1996) Barbosa y Doherty (1988) usan variable de composición transformada, para la representación y análisis de los resultados, las ventajas que trae consigo la reducción del espacio de composición, su método usa curvas residuales que están basadas en balances de materia en forma de ecuaciones diferenciales para calcular el número de etapas en la columna encontrando también la etapa de alimentación.…”