SEPARATIONSEffect of Chemical Kinetics on Feasible Splits forReactive DistillationNitin Chadda, Michael F. Malone, and Michael F. DohertyDept. of Chemical Engineering, University of Massachusetts, Amherst, MA 01003Feasible direct and indirect sharp splits for multicomponent single-feed continuousreacti®e distillation are predicted with a model, in which each column section is repre-sented by a series of cocurrent isobaric flashes. In the limits of no reaction and equilib-rium chemical reaction, the model reduces to con®entional models for distillation lines,and each column section can be represented by the same equations. At intermediatereaction rates, howe®er, the models for the column sections differ, and new results forfixed points and feasible products are obtained. A bifurcation study shows the limits offeasibility, including the influence of flow rate, catalyst le®el and holdup. Unlike distilla-tion without reaction, limited ranges of feasibility in all of these ®ariables are found. Themethod has been applied to fi®e examples, one of which is described in detail. Feasibil-ity predictions are ®alidated by column simulations.IntroductionReactive distillation is potentially attractive whenever thereis a liquid-phase reaction that involves an excess of reactant.In addition to potential reduced capital and energy costs, re-active distillation can lead to higher conversions by overcom-ing chemical equilibrium constraints. For multiple reactionswhere an intermediate is the desired product, reactive distil-lation may also provide higher selectivities. This is achievedby taking advantage of a separation that suppresses side reac-tions. In some cases the reaction also has the effect of ‘‘re-acting away’’ some of the azeotropes, thereby simplifying thephase behavior and avoiding an expensive separationŽ.Doherty and Buzad, 1992 .For a conceptual design of reactive distillation, systematicmethods are needed for deciding its feasibility. We use geo-metric methods that have been used extensively to assess thefeasibility for nonreactive distillation. For nonreactive distil-lation, a number of algorithms can be used to find the feasi-Ž.ble splits. Stichlmair and Herguijuela 1992 calculate theŽ.products at total reflux, while Wahnshafft et al. 1992 andŽ.Fidkowski et al. 1993 use pinch tracking techniques to esti-mate the feasible products for finite as well as total reflux.These methods rely on geometric visualization, so have beenCorrespondence concerning this article should be addressed to M. F. Doherty atthis current address: Dept. of Chemical Engineering, Univ. of California, Santa Bar-bara, CA 93106-5080.applied to ternary mixtures. Algorithms building on theseideas, but that do not rely on visualization, are described byŽ. Ž.Safrit and Westerberg 1997 and Rooks et al. 1998 . Thesemethods can also be applied in the limit of reaction equilib-rium using transformations of the compositions that haveproperties similar to those of mole fractions in nonreactiveŽmixtures Barbosa and Doherty, 1988; Ung and Doherty,.1995; Espinosa et al., 1995 . These is a one-to-one correspon-dence between the real mole fractions and the transformedvariables at chemical equilibrium.Such one-to-one transformations are not known for kineti-cally controlled reactive distillation, although some aspects ofthese transforms remain useful in the kinetic regime. Studiesat finite rates of reaction are important because most reac-tive distillation devices operate in this regime. There are sev-eral approaches available that capture some of the effects offinite reaction rates, such as, geometric design methodsŽBuzad and Doherty, 1994, 1995; Okasinski and Doherty,.Ž.1998 ; mixed integer nonlinear programming MINLP meth-Žods Ciric and Gu, 1994; Papalexandri and Pistikopoulos,.Ž1996; Ismail et al., 1999 ; attainable-region methods Nisoli et.al., 1997; McGregor et al., 1997 ; residue-curverbifurcationŽmethods Rev, 1993; Venimadhavan et al., 1995, 1999; Thiel.Ž.et al., 1997 ; difference-point methods Lee et al., 2000a,b .However, there are few tools that assess the feasibility of re-Žactive mixtures in the kinetic regime. Giessler et al. 1998,March 2001 Vol. 47, No. 3 AIChE Journal590.1999 use static analysis to determine the feasibility of reac-tive columns operated with large internal flows. Chadda et al.Ž.2000 generate feasible product regions at finite rates of re-action for ternary systems. However, that method cannot beextended to treat a larger number of components or multiplereactions.In this article, we describe an algorithm for predicting fea-sible splits for continuous single-feed reactive distillation thatis not limited by the number of reactions are components.The method described here uses minimal information to de-Ž.termine the feasibility of reactive columns: 1 phase equilib-Ž.rium between the components in the mixture, 2 a reaction-Ž.rate model, and 3 feed specification. This is based on a bi-furcation analysis of the fixed points for a cocurrent flash-Ž.cascade model. Unstable nodes ‘‘light species’’ and stableŽ.nodes ‘‘heavy species’’ in the flash-cascade model are candi-date distillate and bottoms products, respectively, from a re-active distillation column. Therefore, we focus our attentionon those splits that are equivalent to the ‘‘direct’’ and ‘‘indi-rect’’ sharp splits in nonreactive distillation. One of the prod-ucts in these sharp splits could be a pure component, anazeotrope, or a kinetic pinch point; the other product will bein material balance with the first.The proposed algorithm is based on1. A bifurcation study to predict the distillate and bottomsproducts for the entire range of reaction rates from the limitof no reaction to the limit of chemical equilibrium. This pro-vides a global view of the sharp-split products from a continu-ous reactive distillation at all rates of reaction.2. Flash calculations and the application of the le®er ruleŽoverall mass balance relating the feed, distillate, and bot-.toms product streams to predict feasible sharp splits for agiven feed condition.We also demonstrate that the feasible sharp splits pre-dicted by the algorithm are in good agreement with columnsimulations. Thus, this algorithm can be used effectively toquickly estimate feasible sharp splits for continuous single-feed reactive distillation.Flash-Cascade ModelŽIn a distillation column, each section rectifying or strip-.ping can be